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Question Find the value of xx that satisfies the equation 10(x+2)=5(x+8)10(x+2) = 5(x+8). Choose from options A-E.

Studdy Solution

STEP 1

Assumptions
1. We are given an equation 10(x+2)=5(x+8)10(x+2) = 5(x+8).
2. We need to solve for the value of xx.

STEP 2

First, we need to distribute the multiplication across the parentheses on both sides of the equation.
10(x+2)=5(x+8)10(x+2) = 5(x+8)

STEP 3

Distribute the 1010 and 55 to the terms inside the parentheses.
10x+20=5x+4010x + 20 = 5x + 40

STEP 4

Now, we want to get all the xx terms on one side of the equation and the constants on the other side. We can do this by subtracting 5x5x from both sides of the equation.
10x+20−5x=5x+40−5x10x + 20 - 5x = 5x + 40 - 5x

STEP 5

Simplify both sides of the equation.
5x+20=405x + 20 = 40

STEP 6

Next, subtract 2020 from both sides of the equation to isolate the xx term.
5x+20−20=40−205x + 20 - 20 = 40 - 20

STEP 7

Simplify both sides of the equation.
5x=205x = 20

STEP 8

To find the value of xx, divide both sides of the equation by 55.
5x5=205\frac{5x}{5} = \frac{20}{5}

STEP 9

Calculate the value of xx.
x=4x = 4
The value of xx is 44, which corresponds to option C.

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