Problem 86 - College Algebra

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

Step 1: Simplify the equation

First, clean up the equation to more easily find \(x\). Distribute the 2 on both sides of the equation: \(2x - 12 = 3x + 4x - 2\). This simplifies to \(2x - 12 = 7x - 2\)

Step 2: Solve for \(x\)

Now, rearrange the equation to isolate \(x\) on one side. To do so, subtract \(7x\) from both sides and add 12 to both sides: \(2x - 7x = -2 + 12\), which simplifies to \(-5x = 10\). Finally, divide by -5 to find the value of \(x\): \(x = -2\)

Step 3: Evaluate the expression

Now that we know that \(x\) equals -2, use this value to evaluate the expression \(x^{2}-x\). Substitute -2 into the expression: \((-2)^{2} - (-2)\), which simplifies to \(4 + 2\)

Step 4: Get the final answer

This simplifies to the final answer of 6. Therefore, \(x^{2}-x\) equals 6 for the value of \(x\) satisfying \(2(x-6)=3 x+2(2 x-1)\)