To solve the equation, we can combine the two fractions on the left side of the equation by finding a common denominator. The common denominator for 2 and 4 is 4, so we can rewrite the equation as:
1/2x + 1/4x = 16
To add the fractions with the same denominator, we can combine the numerators:
(1/2 + 1/4)x = 16
Now, we need to find a common denominator for 2 and 4, which is 4. We can rewrite the equation as:
(2/4 + 1/4)x = 16
Now, we can combine the numerators:
(3/4)x = 16
To isolate x, we can multiply both sides of the equation by the reciprocal of 3/4, which is 4/3:
(4/3)(3/4)x = (4/3)(16)
Simplifying:
x = 64/3
Therefore, the solution to the equation is x = 64/3.
olve the equation.
StartFraction 1 over 2 EndFraction x plus StartFraction 1 over 4 EndFraction x equals 16
(1 point)
Responses
16
16
21.3
21.3
32
32
64
15 answers
no
Apologies for the mistake. Let's go through the solution again.
We have the equation:
1/2x + 1/4x = 16
To combine the fractions on the left side, we need a common denominator, which is 4. We can write the equation as:
2/4x + 1/4x = 16
Now we can add the fractions:
3/4x = 16
To isolate x, we multiply both sides of the equation by the reciprocal of 3/4, which is 4/3:
(4/3)(3/4x) = (4/3)(16)
Simplifying:
1x = 64/3
Therefore, the solution to the equation is x = 64/3.
We have the equation:
1/2x + 1/4x = 16
To combine the fractions on the left side, we need a common denominator, which is 4. We can write the equation as:
2/4x + 1/4x = 16
Now we can add the fractions:
3/4x = 16
To isolate x, we multiply both sides of the equation by the reciprocal of 3/4, which is 4/3:
(4/3)(3/4x) = (4/3)(16)
Simplifying:
1x = 64/3
Therefore, the solution to the equation is x = 64/3.
Solve the equation.
6 minus lower x minus lower x equals 18
(1 point)
Responses
negative 6
Image with alt text: negative 6
6
6
9
9
negative 9
6 minus lower x minus lower x equals 18
(1 point)
Responses
negative 6
Image with alt text: negative 6
6
6
9
9
negative 9
To solve the equation, we can simplify and isolate the variable.
6 - x - x = 18
Combining like terms:
6 - 2x = 18
Next, we want to isolate the variable 'x' by moving the constant term to the other side of the equation. We can do this by subtracting 6 from both sides:
-2x = 18 - 6
Simplifying:
-2x = 12
To solve for 'x', we divide both sides of the equation by -2:
x = 12 / -2
Simplifying:
x = -6
Therefore, the solution to the equation is x = -6.
6 - x - x = 18
Combining like terms:
6 - 2x = 18
Next, we want to isolate the variable 'x' by moving the constant term to the other side of the equation. We can do this by subtracting 6 from both sides:
-2x = 18 - 6
Simplifying:
-2x = 12
To solve for 'x', we divide both sides of the equation by -2:
x = 12 / -2
Simplifying:
x = -6
Therefore, the solution to the equation is x = -6.
Solve the equation.
4 lower x minus three-fifths equals two-fifths
(1 point)
Responses
Fraction is 1 over 5.
Image with alt text: Fraction is 1 over 5.
5 over 5
Image with alt text: 5 over 5
one half
Image with alt text: one half
one-fourth
4 lower x minus three-fifths equals two-fifths
(1 point)
Responses
Fraction is 1 over 5.
Image with alt text: Fraction is 1 over 5.
5 over 5
Image with alt text: 5 over 5
one half
Image with alt text: one half
one-fourth
To solve the equation, we can isolate the variable 'x'.
Starting with the equation:
4x - 3/5 = 2/5
To isolate the term with 'x', we can add 3/5 to both sides of the equation:
4x - 3/5 + 3/5 = 2/5 + 3/5
Simplifying:
4x = 5/5
Since 5/5 is equal to 1, we have:
4x = 1
To solve for 'x', we divide both sides of the equation by 4:
(4x)/4 = 1/4
Simplifying:
x = 1/4
Therefore, the solution to the equation is x = 1/4.
Starting with the equation:
4x - 3/5 = 2/5
To isolate the term with 'x', we can add 3/5 to both sides of the equation:
4x - 3/5 + 3/5 = 2/5 + 3/5
Simplifying:
4x = 5/5
Since 5/5 is equal to 1, we have:
4x = 1
To solve for 'x', we divide both sides of the equation by 4:
(4x)/4 = 1/4
Simplifying:
x = 1/4
Therefore, the solution to the equation is x = 1/4.
Solve the equation.
lower x minus 13 plus 4 lower x equals 22
(1 point)
Responses
1.8
1.8
5
5
7
7
11.7
11.7
lower x minus 13 plus 4 lower x equals 22
(1 point)
Responses
1.8
1.8
5
5
7
7
11.7
11.7
To solve the equation, we can combine like terms and isolate the variable.
Starting with the equation:
x - 13 + 4x = 22
To combine like terms, we add 'x' and '4x':
5x - 13 = 22
Next, we want to isolate the variable 'x' by moving the constant term to the other side of the equation. We can do this by adding 13 to both sides:
5x = 22 + 13
Simplifying:
5x = 35
To solve for 'x', we divide both sides of the equation by 5:
(5x)/5 = 35/5
Simplifying:
x = 7
Therefore, the solution to the equation is x = 7.
Starting with the equation:
x - 13 + 4x = 22
To combine like terms, we add 'x' and '4x':
5x - 13 = 22
Next, we want to isolate the variable 'x' by moving the constant term to the other side of the equation. We can do this by adding 13 to both sides:
5x = 22 + 13
Simplifying:
5x = 35
To solve for 'x', we divide both sides of the equation by 5:
(5x)/5 = 35/5
Simplifying:
x = 7
Therefore, the solution to the equation is x = 7.
Solve the equation.
negative 36 equals negative 6 left parenthesis 2 x minus 14 right parenthesis
(1 point)
Responses
10
10
1.8
1.8
24
24
4
negative 36 equals negative 6 left parenthesis 2 x minus 14 right parenthesis
(1 point)
Responses
10
10
1.8
1.8
24
24
4
To solve the equation, we can simplify and isolate the variable.
Starting with the equation:
-36 = -6(2x - 14)
To simplify, we distribute -6 to the terms inside the parentheses:
-36 = -12x + 84
Next, we want to isolate the term with 'x' by moving the constant term to the other side of the equation. We can do this by subtracting 84 from both sides:
-36 - 84 = -12x
Simplifying:
-120 = -12x
To solve for 'x', we divide both sides of the equation by -12:
(-120) / (-12) = x
Simplifying:
x = 10
Therefore, the solution to the equation is x = 10.
Starting with the equation:
-36 = -6(2x - 14)
To simplify, we distribute -6 to the terms inside the parentheses:
-36 = -12x + 84
Next, we want to isolate the term with 'x' by moving the constant term to the other side of the equation. We can do this by subtracting 84 from both sides:
-36 - 84 = -12x
Simplifying:
-120 = -12x
To solve for 'x', we divide both sides of the equation by -12:
(-120) / (-12) = x
Simplifying:
x = 10
Therefore, the solution to the equation is x = 10.
Solve the equation.
2 plus StartFraction x over negative 10 EndFraction equals StartFraction 2 over 5 EndFraction
(1 point)
Responses
negative 16
Image with alt text: negative 16
negative 24
Image with alt text: negative 24
16
16
24
24
2 plus StartFraction x over negative 10 EndFraction equals StartFraction 2 over 5 EndFraction
(1 point)
Responses
negative 16
Image with alt text: negative 16
negative 24
Image with alt text: negative 24
16
16
24
24
To solve the equation, we can isolate the variable 'x'.
Starting with the equation:
2 + (x/-10) = 2/5
To simplify, we can multiply both sides of the equation by -10 to cancel out the fraction:
-10(2) + (-10)(x/-10) = (-10)(2/5)
Simplifying:
-20 + x = -4
To isolate 'x', we can subtract -20 from both sides:
x - 20 + 20 = -4 + 20
Simplifying:
x = 16
Therefore, the solution to the equation is x = 16.
Starting with the equation:
2 + (x/-10) = 2/5
To simplify, we can multiply both sides of the equation by -10 to cancel out the fraction:
-10(2) + (-10)(x/-10) = (-10)(2/5)
Simplifying:
-20 + x = -4
To isolate 'x', we can subtract -20 from both sides:
x - 20 + 20 = -4 + 20
Simplifying:
x = 16
Therefore, the solution to the equation is x = 16.
You are ordering pizzas for a birthday party and getting them delivered to your house. You order 12 pepperoni pizzas, 8 cheese pizzas, and 4 Hawaiian pizzas. There is a delivery fee of $5.50. If your total comes to $184.54, how much was each pizza? Assume that all types of pizza cost the same amount.
(1 point)
Responses
$7.46
$7.46
$7.69
$7.69
$8.95
$8.95
$12.79
(1 point)
Responses
$7.46
$7.46
$7.69
$7.69
$8.95
$8.95
$12.79
To solve this problem, we need to find the cost of each pizza.
Let's assume the cost of each pizza is 'x'.
The cost of 12 pepperoni pizzas would be 12x.
The cost of 8 cheese pizzas would be 8x.
The cost of 4 Hawaiian pizzas would be 4x.
The total cost of all the pizzas, including the delivery fee, is given as $184.54.
Therefore, we can set up the equation:
12x + 8x + 4x + 5.50 = 184.54
Simplifying:
24x + 5.50 = 184.54
Subtracting 5.50 from both sides:
24x = 179.04
Dividing both sides by 24:
x = 7.46
Therefore, each pizza costs $7.46.
The correct response is $7.46.
Let's assume the cost of each pizza is 'x'.
The cost of 12 pepperoni pizzas would be 12x.
The cost of 8 cheese pizzas would be 8x.
The cost of 4 Hawaiian pizzas would be 4x.
The total cost of all the pizzas, including the delivery fee, is given as $184.54.
Therefore, we can set up the equation:
12x + 8x + 4x + 5.50 = 184.54
Simplifying:
24x + 5.50 = 184.54
Subtracting 5.50 from both sides:
24x = 179.04
Dividing both sides by 24:
x = 7.46
Therefore, each pizza costs $7.46.
The correct response is $7.46.