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QuestionSolve the equation: −2(x−1)=5x+16-2(x-1)=5x+16. Find x=[?]x=[?].

Studdy Solution

STEP 1

Assumptions1. The equation is -(x-1) =5x +16. We are solving for x

STEP 2

First, distribute the -2 on the left side of the equation.
−2(x−1)=−2x+2-2(x-1) = -2x +2

STEP 3

Replace the left side of the equation with the result from the distribution.
−2x+2=5x+16-2x +2 =5x +16

STEP 4

To isolate x, we need to move all terms involving x to one side of the equation and the constants to the other side. Let's start by adding2x to both sides of the equation to eliminate -2x from the left side.
2x−2x+2=x+2x+162x -2x +2 =x +2x +16

STEP 5

implify both sides of the equation.
2=7x+162 =7x +16

STEP 6

Next, subtract16 from both sides of the equation to move the constant from the right side to the left side.
2−16=x+16−162 -16 =x +16 -16

STEP 7

implify both sides of the equation.
−14=7x-14 =7x

STEP 8

Finally, divide both sides of the equation by7 to solve for x.
x=−14/7x = -14 /7

STEP 9

implify the right side of the equation to find the value of x.
x=−2x = -2So, the solution to the equation -2(x-) =5x +16 is x = -2.

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