To solve for x, we need to isolate the x term on one side of the equation.
3x + 2 = x + 8
First, we can subtract x from both sides to eliminate the x term on the right side:
3x - x + 2 = 8
Simplifying the left side gives us:
2x + 2 = 8
Next, we can subtract 2 from both sides to isolate the x term:
2x + 2 - 2 = 8 - 2
Simplifying both sides gives us:
2x = 6
Finally, we can divide both sides by 2 to solve for x:
(2x)/2 = 6/2
Simplifying both sides gives us:
x = 3
Therefore, the solution is x = 3.
C. 3
Solve for x.
3x + 2 = x + 8
A.
1.5
B.
2.5
C.
3
D.
5
11 answers
Which equations have infinitely many solutions? Select TWO that apply.
A. 6(x - 9) = 62-54 + x
B. 5(x8) + 10 = 5(x + 2)
C. 208x62(7-4)
D. 4(x+4) = 2(2x+5) +6
E. 2x + 9 = 18+ 2x
A. 6(x - 9) = 62-54 + x
B. 5(x8) + 10 = 5(x + 2)
C. 208x62(7-4)
D. 4(x+4) = 2(2x+5) +6
E. 2x + 9 = 18+ 2x
To determine if an equation has infinitely many solutions, we need to check if both sides of the equation are equal for any value of x.
Let's examine each option:
A. 6(x - 9) = 62-54 + x
Simplifying both sides gives us:
6x - 54 = 8 + x
If we continue simplifying, we can see that we have an x term on both sides. However, we do not have a number that can be canceled out. Therefore, this equation does not have infinitely many solutions.
B. 5(x8) + 10 = 5(x + 2)
Simplifying both sides gives us:
5x + 40 + 10 = 5x + 10
If we continue simplifying, we can see that we have an x term on both sides. However, we also have a number, 40, that can be canceled out. Therefore, this equation has infinitely many solutions.
C. 208x62(7-4)
This is not an equation, but an expression. It does not have an equal sign, so we cannot determine if it has any solutions.
D. 4(x+4) = 2(2x+5) +6
Simplifying both sides gives us:
4x + 16 = 4x + 10 + 6
If we continue simplifying, we can see that we have an x term on both sides. However, we also have numbers, 16 and 16, that can be canceled out. Therefore, this equation has infinitely many solutions.
E. 2x + 9 = 18+ 2x
Simplifying both sides gives us:
2x + 9 = 18 + 2x
If we continue simplifying, we can see that we have an x term on both sides. However, there are no numbers that can be canceled out. Therefore, this equation does not have infinitely many solutions.
In summary, the equations that have infinitely many solutions are:
B. 5(x8) + 10 = 5(x + 2)
D. 4(x+4) = 2(2x+5) +6
Let's examine each option:
A. 6(x - 9) = 62-54 + x
Simplifying both sides gives us:
6x - 54 = 8 + x
If we continue simplifying, we can see that we have an x term on both sides. However, we do not have a number that can be canceled out. Therefore, this equation does not have infinitely many solutions.
B. 5(x8) + 10 = 5(x + 2)
Simplifying both sides gives us:
5x + 40 + 10 = 5x + 10
If we continue simplifying, we can see that we have an x term on both sides. However, we also have a number, 40, that can be canceled out. Therefore, this equation has infinitely many solutions.
C. 208x62(7-4)
This is not an equation, but an expression. It does not have an equal sign, so we cannot determine if it has any solutions.
D. 4(x+4) = 2(2x+5) +6
Simplifying both sides gives us:
4x + 16 = 4x + 10 + 6
If we continue simplifying, we can see that we have an x term on both sides. However, we also have numbers, 16 and 16, that can be canceled out. Therefore, this equation has infinitely many solutions.
E. 2x + 9 = 18+ 2x
Simplifying both sides gives us:
2x + 9 = 18 + 2x
If we continue simplifying, we can see that we have an x term on both sides. However, there are no numbers that can be canceled out. Therefore, this equation does not have infinitely many solutions.
In summary, the equations that have infinitely many solutions are:
B. 5(x8) + 10 = 5(x + 2)
D. 4(x+4) = 2(2x+5) +6
A salesman makes both a base salary and also a commission, which is a percentage of what he sells. Each month, if his sales total s dollars, he makes a total of 2,000 + 0.1s dollars. What does 2,000 represent?
A.
his monthly base salary in dollars
B.
the amount of his monthly sales in dollars
C.
his total monthly pay in dollars
D.
his monthly commission in dollars
A.
his monthly base salary in dollars
B.
the amount of his monthly sales in dollars
C.
his total monthly pay in dollars
D.
his monthly commission in dollars
The statement "2,000 represents" implies that we are looking for the meaning or representational value of 2,000 in the given context.
In this case, the salesman makes a total of 2,000 + 0.1s dollars each month, where s represents the amount of his sales in dollars.
The 2,000 in this expression refers to the base salary, which is not dependent on the amount of sales. It is a fixed amount that the salesman receives each month regardless of the sales he makes.
Therefore, the answer is:
A. his monthly base salary in dollars
In this case, the salesman makes a total of 2,000 + 0.1s dollars each month, where s represents the amount of his sales in dollars.
The 2,000 in this expression refers to the base salary, which is not dependent on the amount of sales. It is a fixed amount that the salesman receives each month regardless of the sales he makes.
Therefore, the answer is:
A. his monthly base salary in dollars
The value of a baseball card in dollars has been found to be 0.15y + 0.35, where y is the number of years since it was released. By how much is the baseball card's value increasing per year?
A.
$0.15
B.
$0.35
C.
15%
D.
35%
A.
$0.15
B.
$0.35
C.
15%
D.
35%
To determine the rate at which the baseball card's value is increasing per year, we need to look at the coefficient of y in the given expression.
The expression 0.15y + 0.35 represents the value of the baseball card in dollars, where y is the number of years since it was released.
The coefficient of y, 0.15, indicates the amount by which the value of the baseball card increases per year. Therefore, the answer is:
A. $0.15
The expression 0.15y + 0.35 represents the value of the baseball card in dollars, where y is the number of years since it was released.
The coefficient of y, 0.15, indicates the amount by which the value of the baseball card increases per year. Therefore, the answer is:
A. $0.15
Multiple Choice Question
Manipulate the equation y=5x-11 so that it is written in terms of x. Which equation is equivalent to y=5x-11?
A.
x=(11/y) -5
B.
x=y+11/5
C. y+11/5
D.
x=(y/5) +11
Manipulate the equation y=5x-11 so that it is written in terms of x. Which equation is equivalent to y=5x-11?
A.
x=(11/y) -5
B.
x=y+11/5
C. y+11/5
D.
x=(y/5) +11
To manipulate the equation y = 5x - 11 so that it is written in terms of x, we need to isolate the variable x.
The equivalent equation can be found by performing the following steps:
First, add 11 to both sides of the equation:
y + 11 = 5x
Next, divide both sides of the equation by 5:
(y + 11)/5 = x
Now, we have isolated x on one side of the equation, so the answer is:
B. x = (y + 11)/5
The equivalent equation can be found by performing the following steps:
First, add 11 to both sides of the equation:
y + 11 = 5x
Next, divide both sides of the equation by 5:
(y + 11)/5 = x
Now, we have isolated x on one side of the equation, so the answer is:
B. x = (y + 11)/5
Multiple Choice Question
Charity is buying peaches at the store. The cost of the peaches are $1.30 per pound. If she has $6.50 to spend on peaches, how many pounds (x) can she buy?
Set up an equation to solve the problem.
A.
1.30x=6.50
B.
1.30+x=6.50
C.
1.30/6.50=x
D.
6.50x=1.30
Charity is buying peaches at the store. The cost of the peaches are $1.30 per pound. If she has $6.50 to spend on peaches, how many pounds (x) can she buy?
Set up an equation to solve the problem.
A.
1.30x=6.50
B.
1.30+x=6.50
C.
1.30/6.50=x
D.
6.50x=1.30
To set up an equation to solve the problem, we need to express the total cost of the peaches in terms of the number of pounds Charity can buy.
Let x represent the number of pounds of peaches.
The cost of the peaches per pound is $1.30, and Charity has $6.50 to spend. To find the total cost of the peaches, we multiply the cost per pound by the number of pounds:
Total cost = Cost per pound × Number of pounds
Total cost = 1.30x
Now, we have set up the equation to solve the problem:
A. 1.30x = 6.50
Let x represent the number of pounds of peaches.
The cost of the peaches per pound is $1.30, and Charity has $6.50 to spend. To find the total cost of the peaches, we multiply the cost per pound by the number of pounds:
Total cost = Cost per pound × Number of pounds
Total cost = 1.30x
Now, we have set up the equation to solve the problem:
A. 1.30x = 6.50