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QuestionSolve the equation: 7[2−(3+2x)]−2x=−9+2(1−8x)7[2-(3+2 x)]-2 x=-9+2(1-8 x).

Studdy Solution

STEP 1

Assumptions1. We are given the equation 7[−(3+x)]−x=−9+(1−8x)7[-(3+x)]-x=-9+(1-8x). We are to solve for the variable xx

STEP 2

First, we need to simplify the equation by distributing the multiplication across the terms in the brackets.
7[2−(+2x)]−2x=7[2−−2x]−2x=7[−1−2x]−2x=−7−14x−2x7[2-(+2x)]-2x =7[2--2x]-2x =7[-1-2x]-2x = -7-14x-2x

STEP 3

Similarly, distribute the multiplication on the right side of the equation.
−9+2(1−8x)=−9+2−16x=−7−16x-9+2(1-8x) = -9+2-16x = -7-16x

STEP 4

Now, we have the simplified equation.
−7−14x−2x=−7−16x-7-14x-2x = -7-16x

STEP 5

Combine like terms on both sides of the equation.
−7−16x=−7−16x-7-16x = -7-16x

STEP 6

Subtract −- from both sides of the equation.
−16x=−16x-16x = -16x

STEP 7

Divide both sides of the equation by −16-16 to solve for xx.
x=xx = xThe solution is that all real numbers are solutions, as the equation is an identity, meaning it is true for all values of xx.

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