To solve the equation x - 6 = 8, you need to isolate the variable x.
Add 6 to both sides of the equation:
x - 6 + 6 = 8 + 6
This simplifies to:
x = 14
So the solution to the equation is x = 14.
x – 6 = 8
47 answers
y + 5 = –12
To solve the equation y + 5 = -12, you need to isolate the variable y.
Subtract 5 from both sides of the equation:
y + 5 - 5 = -12 - 5
This simplifies to:
y = -17
So the solution to the equation is y = -17.
Subtract 5 from both sides of the equation:
y + 5 - 5 = -12 - 5
This simplifies to:
y = -17
So the solution to the equation is y = -17.
one-fourtha = 3
To solve the equation one-fourth a = 3, you need to isolate the variable a.
Multiply both sides of the equation by 4 to get rid of the fraction:
4 * (one-fourth a) = 4 * 3
This simplifies to:
a = 12
So the solution to the equation is a = 12.
Multiply both sides of the equation by 4 to get rid of the fraction:
4 * (one-fourth a) = 4 * 3
This simplifies to:
a = 12
So the solution to the equation is a = 12.
–2c = –18
To solve the equation -2c = -18, you need to isolate the variable c.
Divide both sides of the equation by -2:
(-2c) / -2 = (-18) / -2
This simplifies to:
c = 9
So the solution to the equation is c = 9.
Divide both sides of the equation by -2:
(-2c) / -2 = (-18) / -2
This simplifies to:
c = 9
So the solution to the equation is c = 9.
two-thirdsx = 6
To solve the equation (two-thirds)x = 6, you need to isolate the variable x.
Multiply both sides of the equation by the reciprocal of two-thirds, which is three-halves (2/3):
(two-thirds)x * (3/2) = 6 * (3/2)
Simplifying, we have:
x = 9
So the solution to the equation is x = 9.
Multiply both sides of the equation by the reciprocal of two-thirds, which is three-halves (2/3):
(two-thirds)x * (3/2) = 6 * (3/2)
Simplifying, we have:
x = 9
So the solution to the equation is x = 9.
6.5 = –3 + n
To solve the equation 6.5 = -3 + n, you need to isolate the variable n.
Subtract -3 from both sides of the equation:
6.5 - (-3) = -3 + n - (-3)
Simplifying, we have:
6.5 + 3 = -3 + n + 3
This simplifies to:
9.5 = n
So the solution to the equation is n = 9.5.
Subtract -3 from both sides of the equation:
6.5 - (-3) = -3 + n - (-3)
Simplifying, we have:
6.5 + 3 = -3 + n + 3
This simplifies to:
9.5 = n
So the solution to the equation is n = 9.5.
start fraction x over 4 end fraction = Start Fraction 12 over 6 End Fraction
To solve the equation $\frac{x}{4} = \frac{12}{6}$, you need to simplify the fractions and isolate the variable $x$.
First, simplify the fraction $\frac{12}{6}$:
$\frac{12}{6} = 2$
The equation now becomes:
$\frac{x}{4} = 2$
To isolate $x$, multiply both sides of the equation by 4:
$\frac{x}{4} \cdot 4 = 2 \cdot 4$
This simplifies to:
$x = 8$
So the solution to the equation is $x = 8$.
First, simplify the fraction $\frac{12}{6}$:
$\frac{12}{6} = 2$
The equation now becomes:
$\frac{x}{4} = 2$
To isolate $x$, multiply both sides of the equation by 4:
$\frac{x}{4} \cdot 4 = 2 \cdot 4$
This simplifies to:
$x = 8$
So the solution to the equation is $x = 8$.
You need to make 18 cupcakes for a birthday party. You have already made 11. How many more cupcakes do you need to make? Write an equation and solve.
To find out how many more cupcakes you need to make, you can subtract the number of cupcakes you have already made from the total number of cupcakes needed.
Let x represent the number of additional cupcakes you need to make.
The equation to represent the situation is: cupcakes needed - cupcakes already made = cupcakes to be made
Substituting the given values, we have: 18 - 11 = x
Simplifying the equation, we have: 7 = x
Therefore, you need to make 7 more cupcakes for the birthday party.
Let x represent the number of additional cupcakes you need to make.
The equation to represent the situation is: cupcakes needed - cupcakes already made = cupcakes to be made
Substituting the given values, we have: 18 - 11 = x
Simplifying the equation, we have: 7 = x
Therefore, you need to make 7 more cupcakes for the birthday party.
Which of the following is a solution to the equation y = 3x – 1?
To determine which of the following options is a solution to the equation y = 3x - 1, you need to substitute the values given for x and y into the equation and check if it holds true.
Let's consider the options one by one and see if they satisfy the equation:
1) (x = 2, y = 5):
Substituting x = 2 and y = 5 into the equation, we have:
5 = 3(2) - 1
5 = 6 - 1
5 = 5
Since both sides of the equation are equal, (x = 2, y = 5) satisfies the equation.
2) (x = 0, y = -1):
Substituting x = 0 and y = -1 into the equation, we have:
-1 = 3(0) - 1
-1 = -1
Again, both sides of the equation are equal, so (x = 0, y = -1) satisfies the equation.
3) (x = -1, y = 4):
Substituting x = -1 and y = 4 into the equation, we have:
4 = 3(-1) - 1
4 = -3 - 1
4 = -4
The equation does not hold true in this case, so (x = -1, y = 4) is not a solution to the equation.
Therefore, the options (x = 2, y = 5) and (x = 0, y = -1) are solutions to the equation y = 3x - 1.
Let's consider the options one by one and see if they satisfy the equation:
1) (x = 2, y = 5):
Substituting x = 2 and y = 5 into the equation, we have:
5 = 3(2) - 1
5 = 6 - 1
5 = 5
Since both sides of the equation are equal, (x = 2, y = 5) satisfies the equation.
2) (x = 0, y = -1):
Substituting x = 0 and y = -1 into the equation, we have:
-1 = 3(0) - 1
-1 = -1
Again, both sides of the equation are equal, so (x = 0, y = -1) satisfies the equation.
3) (x = -1, y = 4):
Substituting x = -1 and y = 4 into the equation, we have:
4 = 3(-1) - 1
4 = -3 - 1
4 = -4
The equation does not hold true in this case, so (x = -1, y = 4) is not a solution to the equation.
Therefore, the options (x = 2, y = 5) and (x = 0, y = -1) are solutions to the equation y = 3x - 1.
Which equation represents the pattern in the table below?
Sal’s and Carrie’s Ages
Sal
3
5
8
13
15
Carrie
7
9
12
17
19
Sal’s and Carrie’s Ages
Sal
3
5
8
13
15
Carrie
7
9
12
17
19
Looking at the table, we can see that Sal's age is increasing by 2 each time, while Carrie's age is increasing by 2 as well. To represent this pattern, we can write the equation:
Sal's age = 2 x (Carrie's age) - 1
So the equation that represents the pattern in the table is Sal's age = 2 x (Carrie's age) - 1.
Sal's age = 2 x (Carrie's age) - 1
So the equation that represents the pattern in the table is Sal's age = 2 x (Carrie's age) - 1.
Which equation matches the statement: “The sum of –4x and 2 is 9”?
To represent the statement "The sum of -4x and 2 is 9" as an equation, we can write:
-4x + 2 = 9
Therefore, the equation that matches the statement is -4x + 2 = 9.
-4x + 2 = 9
Therefore, the equation that matches the statement is -4x + 2 = 9.
x – 6 = –18
To solve the equation x - 6 = -18, you need to isolate the variable x.
Add 6 to both sides of the equation:
x - 6 + 6 = -18 + 6
This simplifies to:
x = -12
So the solution to the equation is x = -12.
Add 6 to both sides of the equation:
x - 6 + 6 = -18 + 6
This simplifies to:
x = -12
So the solution to the equation is x = -12.
4x + 3 = 47
To solve the equation 4x + 3 = 47, you need to isolate the variable x.
First, subtract 3 from both sides of the equation:
4x + 3 - 3 = 47 - 3
This simplifies to:
4x = 44
Next, divide both sides of the equation by 4:
4x/4 = 44/4
This simplifies to:
x = 11
So the solution to the equation is x = 11.
First, subtract 3 from both sides of the equation:
4x + 3 - 3 = 47 - 3
This simplifies to:
4x = 44
Next, divide both sides of the equation by 4:
4x/4 = 44/4
This simplifies to:
x = 11
So the solution to the equation is x = 11.
one-thirdx = 12
To solve the equation (one-third)x = 12, you need to isolate the variable x.
Multiply both sides of the equation by the reciprocal of one-third, which is three:
(one-third)x * 3 = 12 * 3
This simplifies to:
x = 36
So the solution to the equation is x = 36.
Multiply both sides of the equation by the reciprocal of one-third, which is three:
(one-third)x * 3 = 12 * 3
This simplifies to:
x = 36
So the solution to the equation is x = 36.
3x + 3 = 21
To solve the equation 3x + 3 = 21, you need to isolate the variable x.
First, subtract 3 from both sides of the equation:
3x + 3 - 3 = 21 - 3
This simplifies to:
3x = 18
Next, divide both sides of the equation by 3:
3x/3 = 18/3
This simplifies to:
x = 6
So the solution to the equation is x = 6.
First, subtract 3 from both sides of the equation:
3x + 3 - 3 = 21 - 3
This simplifies to:
3x = 18
Next, divide both sides of the equation by 3:
3x/3 = 18/3
This simplifies to:
x = 6
So the solution to the equation is x = 6.
. Start Fraction 3 over 2 End Fractionx – 4 = 16
To solve the equation $\frac{3}{2}x - 4 = 16$, you need to isolate the variable x.
First, add 4 to both sides of the equation:
$\frac{3}{2}x - 4 + 4 = 16 + 4$
This simplifies to:
$\frac{3}{2}x = 20$
Next, multiply both sides of the equation by the reciprocal of $\frac{3}{2}$, which is $\frac{2}{3}$:
$\left(\frac{3}{2}x\right) \cdot \left(\frac{2}{3}\right) = 20 \cdot \frac{2}{3}$
This simplifies to:
$x = \frac{40}{3}$
So the solution to the equation is $x = \frac{40}{3}$.
First, add 4 to both sides of the equation:
$\frac{3}{2}x - 4 + 4 = 16 + 4$
This simplifies to:
$\frac{3}{2}x = 20$
Next, multiply both sides of the equation by the reciprocal of $\frac{3}{2}$, which is $\frac{2}{3}$:
$\left(\frac{3}{2}x\right) \cdot \left(\frac{2}{3}\right) = 20 \cdot \frac{2}{3}$
This simplifies to:
$x = \frac{40}{3}$
So the solution to the equation is $x = \frac{40}{3}$.
The equation 9.95 + 0.30s = c gives the cost c in dollars that a website charges for downloading songs. The variable s stands for the number of songs downloaded. Find the cost of downloading 35 songs.
To find the cost of downloading 35 songs, you need to substitute the value of s = 35 into the equation.
The equation 9.95 + 0.30s = c represents the cost c in dollars for downloading songs, with s representing the number of songs.
Substituting s = 35 into the equation, we have:
c = 9.95 + 0.30(35)
Simplifying, we get:
c = 9.95 + 10.50
This further simplifies to:
c = 20.45
Therefore, the cost of downloading 35 songs would be $20.45.
The equation 9.95 + 0.30s = c represents the cost c in dollars for downloading songs, with s representing the number of songs.
Substituting s = 35 into the equation, we have:
c = 9.95 + 0.30(35)
Simplifying, we get:
c = 9.95 + 10.50
This further simplifies to:
c = 20.45
Therefore, the cost of downloading 35 songs would be $20.45.
You have $27 to spend at the mall and a coupon for $6 off at your favorite store. A t-shirt costs $11. How many t-shirts can you buy using your coupon and money?
To find out how many t-shirts you can buy, you need to consider the amount of money you have after applying the coupon.
First, subtract the $6 coupon from your total amount of money:
$27 - $6 = $21
Now, calculate how many t-shirts you can buy with $21 by dividing the amount of money you have by the cost of a t-shirt:
$21 ÷ $11 = 1.909
Since you cannot buy a fraction of a t-shirt, you can buy a maximum of 1 t-shirt using your coupon and money.
First, subtract the $6 coupon from your total amount of money:
$27 - $6 = $21
Now, calculate how many t-shirts you can buy with $21 by dividing the amount of money you have by the cost of a t-shirt:
$21 ÷ $11 = 1.909
Since you cannot buy a fraction of a t-shirt, you can buy a maximum of 1 t-shirt using your coupon and money.
5 = t/2 – 3?
To solve the equation 5 = t/2 - 3, you need to isolate the variable t.
First, add 3 to both sides of the equation:
5 + 3 = t/2 - 3 + 3
This simplifies to:
8 = t/2
Next, multiply both sides of the equation by 2 to eliminate the fraction:
2 * 8 = 2 * (t/2)
This simplifies to:
16 = t
So the solution to the equation is t = 16.
First, add 3 to both sides of the equation:
5 + 3 = t/2 - 3 + 3
This simplifies to:
8 = t/2
Next, multiply both sides of the equation by 2 to eliminate the fraction:
2 * 8 = 2 * (t/2)
This simplifies to:
16 = t
So the solution to the equation is t = 16.
You are making a bulletin board to advertise community service opportunities in your town. You plan to use one quarter of a sheet of construction paper for each ad. You need four full sheets of construction paper for a title banner. You have 18 sheets of construction paper. How many ads can you make?
To determine how many ads you can make, you need to calculate the total number of ads you can create using the available sheets of construction paper.
First, let's calculate the number of ads that can be made from the 4 full sheets of construction paper for the title banner:
4 sheets x 4 ads per sheet = 16 ads
Next, subtract the number of sheets used for the title banner from the total number of sheets available:
18 sheets - 4 sheets = 14 sheets
Since each ad requires one-quarter of a sheet of construction paper, divide the remaining sheets by 1/4 to find the number of ads that can be made:
14 sheets ÷ (1/4 sheet per ad) = 56 ads
Therefore, you can make a total of 56 ads using the available construction paper.
First, let's calculate the number of ads that can be made from the 4 full sheets of construction paper for the title banner:
4 sheets x 4 ads per sheet = 16 ads
Next, subtract the number of sheets used for the title banner from the total number of sheets available:
18 sheets - 4 sheets = 14 sheets
Since each ad requires one-quarter of a sheet of construction paper, divide the remaining sheets by 1/4 to find the number of ads that can be made:
14 sheets ÷ (1/4 sheet per ad) = 56 ads
Therefore, you can make a total of 56 ads using the available construction paper.
What is the solution of 6 = x – 2 ?
4
4
To find the solution to the equation 6 = x - 2, you need to isolate the variable x.
Start by adding 2 to both sides of the equation:
6 + 2 = x - 2 + 2
Simplifying, we have:
8 = x
So the solution to the equation is x = 8.
Start by adding 2 to both sides of the equation:
6 + 2 = x - 2 + 2
Simplifying, we have:
8 = x
So the solution to the equation is x = 8.
Which of the following characteristics identifies Egypt as a nation-state?
The term "nation-state" refers to a country or state that is primarily defined by a shared cultural or ethnic identity of its people.
Of the following characteristics, the one that identifies Egypt as a nation-state is its shared cultural identity. Egypt has a long history and rich cultural heritage, with its ancient Egyptian civilization being one of the oldest and most influential in human history. The majority of the population in Egypt is ethnically Egyptian, and their shared cultural heritage, history, language, and traditions contribute to the nation's identity as a nation-state.
Of the following characteristics, the one that identifies Egypt as a nation-state is its shared cultural identity. Egypt has a long history and rich cultural heritage, with its ancient Egyptian civilization being one of the oldest and most influential in human history. The majority of the population in Egypt is ethnically Egyptian, and their shared cultural heritage, history, language, and traditions contribute to the nation's identity as a nation-state.
Which of the following nation-states was one of the first nation-states established?
Among the following options, the nation-state that is considered one of the first established nation-states is France. France emerged as a nation-state during the Middle Ages and played a significant role in the development of the nation-state concept. It experienced the consolidation of power under a central authority, developed strong cultural and linguistic identity, established a system of government, and had territorial sovereignty, combining elements that characterize a nation-state.
Draw a conclusion about the role of war in uniting Germany.
Based on historical evidence, it can be concluded that war played a significant role in uniting Germany. Prior to its unification in 1871, Germany was a collection of separate states and territories, each with its own ruler and government. However, a series of wars and conflicts helped pave the way for the eventual unification of Germany.
One notable conflict was the Franco-Prussian War of 1870-1871, in which the Kingdom of Prussia and its allies successfully fought against France. The war resulted in a decisive Prussian victory and the subsequent formation of the German Empire under the leadership of Prussia's Chancellor, Otto von Bismarck. This war is often considered a pivotal moment in German history, as it led to the formal unification of the various German states into a single political entity.
Additionally, earlier conflicts such as the Napoleonic Wars and the Wars of German Unification also contributed to the process of unification by reshaping political alliances, weakening existing power structures, and fostering a sense of national identity and pride among the German people.
Overall, it can be concluded that war played a significant role in uniting Germany, as various conflicts contributed to the consolidation of German territories and the establishment of a unified German state.
One notable conflict was the Franco-Prussian War of 1870-1871, in which the Kingdom of Prussia and its allies successfully fought against France. The war resulted in a decisive Prussian victory and the subsequent formation of the German Empire under the leadership of Prussia's Chancellor, Otto von Bismarck. This war is often considered a pivotal moment in German history, as it led to the formal unification of the various German states into a single political entity.
Additionally, earlier conflicts such as the Napoleonic Wars and the Wars of German Unification also contributed to the process of unification by reshaping political alliances, weakening existing power structures, and fostering a sense of national identity and pride among the German people.
Overall, it can be concluded that war played a significant role in uniting Germany, as various conflicts contributed to the consolidation of German territories and the establishment of a unified German state.