Question

8x−5=3x+20.

Answer 1

10x+5=7x−16.

Answer 2

−12x+20=−10x+32.

Answer 3

ax+3=33.

Answer 4

The volume of a rectangular prism can be calculated with the formula V=lwh, where V is the volume, l is the length, w is the width, and h is the height. If a rectangular prism has a volume of 90 ft.3, length of 3 ft., and height of 12 ft., what is its width? Enter your answer as a decimal.

Answer 5

To solve the equation 8x - 5 = 3x + 20, we want to isolate the variable x.

Step 1: Start by subtracting 3x from both sides of the equation to eliminate the 3x term on the right side:
8x - 5 - 3x = 3x + 20 - 3x
5x - 5 = 20

Step 2: Next, add 5 to both sides to move the constant term -5 to the right side:
5x - 5 + 5 = 20 + 5
5x = 25

Step 3: Finally, divide both sides by 5 to solve for x:
5x/5 = 25/5
x = 5

The solution to the equation 8x - 5 = 3x + 20 is x = 5.

Answer 6

To solve the equation 10x + 5 = 7x - 16, we want to isolate the variable x.

Step 1: Start by subtracting 7x from both sides of the equation to eliminate the 7x term on the right side:
10x + 5 - 7x = 7x - 16 - 7x
3x + 5 = -16

Step 2: Next, subtract 5 from both sides to move the constant term 5 to the right side:
3x + 5 - 5 = -16 - 5
3x = -21

Step 3: Finally, divide both sides by 3 to solve for x:
3x/3 = -21/3
x = -7

The solution to the equation 10x + 5 = 7x - 16 is x = -7.

Answer 7

To solve the equation -12x + 20 = -10x + 32, we want to isolate the variable x.

Step 1: Start by subtracting -10x from both sides of the equation to eliminate the -10x term on the right side:
-12x + 20 - (-10x) = -10x + 32 - (-10x)
-12x + 20 + 10x = -10x + 32 + 10x
-2x + 20 = 32

Step 2: Next, subtract 20 from both sides to move the constant term 20 to the right side:
-2x + 20 - 20 = 32 - 20
-2x = 12

Step 3: Finally, divide both sides by -2 to solve for x:
-2x / -2 = 12 / -2
x = -6

The solution to the equation -12x + 20 = -10x + 32 is x = -6.

Answer 8

To solve the equation ax + 3 = 33, we want to isolate the variable x.

Step 1: Start by subtracting 3 from both sides of the equation to move the constant term 3 to the right side:
ax + 3 - 3 = 33 - 3
ax = 30

Step 2: Next, divide both sides by a to solve for x:
ax / a = 30 / a
x = 30/a

The solution to the equation ax + 3 = 33 is x = 30/a.

Answer 9

To find the width of the rectangular prism, we will rearrange the formula V = lwh to solve for w.

Given:
V = 90 ft^3 (volume)
l = 3 ft (length)
h = 12 ft (height)

Substituting the given values into the formula:
90 = 3w * 12

We can simplify the equation:
90 = 36w

To solve for w, divide both sides of the equation by 36:
90 / 36 = 36w / 36
2.5 = w

Therefore, the width of the rectangular prism is 2.5 feet.