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QuestionSolve the equation 4x+2=2(5−2x)4x + 2 = 2(5 - 2x).

Studdy Solution

STEP 1

Assumptions1. We are given the equation 4x+=(5−x)4x + =(5 -x). We are solving for the variable xx

STEP 2

We start by expanding the right side of the equation.
2(5−2x)=2×5−2×2x2(5 -2x) =2 \times5 -2 \times2x

STEP 3

Perform the multiplication to simplify the right side of the equation.
2×5−2×2x=10−x2 \times5 -2 \times2x =10 -x

STEP 4

Now, substitute the simplified right side of the equation back into the original equation.
4x+2=10−4x4x +2 =10 -4x

STEP 5

To isolate xx, we need to get all terms involving xx on one side of the equation and the constants on the other side. Let's start by adding 4x4x to both sides of the equation.
4x+4x+2=10−4x+4x4x +4x +2 =10 -4x +4x

STEP 6

implify both sides of the equation.
8x+2=108x +2 =10

STEP 7

Next, subtract 22 from both sides of the equation to isolate xx on one side.
x+2−2=10−2x +2 -2 =10 -2

STEP 8

implify both sides of the equation.
8x=88x =8

STEP 9

Finally, divide both sides of the equation by 88 to solve for xx.
8x8=88\frac{8x}{8} = \frac{8}{8}

STEP 10

implify both sides of the equation to find the value of xx.
x=x =The solution to the equation 4x+2=2(5−2x)4x +2 =2(5 -2x) is x=x =.

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