Problem 82 - Introductory Algebra for College Students

Question

If \(\frac{3 x}{2}+\frac{3 x}{4}=\frac{x}{4}-4,\) evaluate \(x^{2}-x\)

Step-by-Step Solution

Answer

The evaluated result of the expression \(x^{2}-x\) is 20

Step 1: Simplify the left hand side of the equation

Combine like terms on the left side of the equation. This results in \(\frac{5x}{4} = \frac{x}{4} - 4\)

Step 2: Move \(\frac{x}{4}\) from the right to the left side of the equation

Subtract \(\frac{x}{4}\) from both sides. This results to \(\frac{4x}{4} = -4 \) or \(x=-4\)

Step 3: Substitute the value of \(x\) in \(x^{2}-x\)

Substitute \(x=-4\) in the expression \(x^{2}-x\) to solve for its value. This results to \((-4)^{2}-(-4) = 16+4 = 20\)