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Chapter 6: Problem 93

Evaluate \(x^{2}-x\) for the value of \(x\) satisfying \(4(x-2)+2=4 x-2(2-x)\).

Short Answer

Expert verified
The value of the expression \(x^{2}-x\) for the given x is 30.

Step by step solution

01

Simplify the Given Equations

First, simplify both sides of the given equation:Left side: \(4(x-2) + 2 = 4x - 8 + 2 = 4x - 6\)Right side: \(4x - 2(2 - x) = 4x - 4 + 2x = 6x - 4\)So, the given equation becomes \(4x - 6 = 6x - 4\).
02

Solve for x

Solve the obtained equation \(4x - 6 = 6x - 4\). First, rearrange the equation so the terms involving x are on one side and the constants are on the other side, which leads to \(4x - 6x = 4 - (-6)\), simplified to \(-2x = 10\).Then, divide by -2 to solve for x: \(x = 10/-2 = -5\).
03

Plug x into the Expression

After determining the value of \(x = -5\), apply it to the equation \(x^{2}-x\) so as to find the result. The expression now becomes \((-5)^{2} - (-5) = 25 + 5 = 30\)

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