Problem 88 - College Algebra Essentials

Question

Will help you prepare for the material covered in the next section. Multiply and simplify: \(12\left(\frac{x+2}{4}-\frac{x-1}{3}\right)\)

Step-by-Step Solution

Answer

The simplified form of the given expression is \(-x+10\).

Step 1: Distribute the Multiplication

First, distribute the multiplication operation over the difference operation: \(12\left(\frac{x+2}{4}-\frac{x-1}{3}\right) = 12\left(\frac{x+2}{4}\right) - 12\left(\frac{x-1}{3}\right)\)

Step 2: Multiply Each Term

Next, break down the operations and follow the order of operation: \(=3(x+2) - 4(x-1)\)

Step 3: Expand the Algebraic Expressions

Further simplify by expanding the brackets: \(=3x+6 -4x +4\)

Step 4: Combine Like Terms

Lastly, combine like terms to further simplify the expression: \(=-x+10\)