Problem 86 - College Algebra Essentials

Question

Evaluate \(x^{2}-x\) for the value of \(x\) satisfying \(2(x-6)=3 x+2(2 x-1)\).

Step-by-Step Solution

Answer

The value of the expression \(x^{2}-x\) for the value of \(x\) that satisfies the equation \(2(x-6)=3 x+2(2 x-1)\) is 5.04.

Step 1: Simplify Both Sides of the Equation

Start by simplifying both sides of the equation \(2(x-6)=3x+2(2x-1)\). This gives us \(2x - 12 = 3x + 4x - 2\). Further simplifying gives \(2x - 12 = 7x - 2\).

Step 2: Solve the Equation

Rearrange the terms to have all \(x\)s on one side of the equation and numbers on the other side to find the solution. This gives us \(7x - 2x = 12 + 2\). Simplifying further gives us \(5x = 14\). So, dividing by 5 gives \(x = 14/5=2.8\).

Step 3: Substitute the Value of \( x \) into the Expression

Now that we have \(x = 2.8\), we need to substitute this back into the expression \(x^{2}-x\). So our new expression becomes \((2.8)^{2} - 2.8\). This results in \(7.84 - 2.8 = 5.04.\)