Problem 93 - College Algebra Essentials

Question

Simplify each algebraic expression. $$7-4[3-(4 y-5)]$$

Step-by-Step Solution

Answer

The simplified form of the expression is \(16y - 25\)

Step 1: Distribute the Negative

Distribute -4 inside the square brackets, resulting in the expression: \(7 - 4\times3 + 4\times4y - 4\times5\). Remember the rule: negative times positive gives negative and negative times negative gives positive. Don't forget to keep the brackets until all elements inside are fully simplified.

Step 2: Simplify Inside the Square Brackets

Carry out the multiplications inside the brackets, which gives: \(7 - 12 + 16y - 20\). Now, the brackets can be removed given that the expression inside is fully simplified. The expression becomes: \(7 - 12 + 16y - 20\).

Step 3: Combine 'Like' Terms

Simplify by gathering the 'y' terms and the constants separately. The expression becomes: \(16y + 7 -12 -20\).

Step 4: Simplify the Expression

By performing the remaining arithmetic operations, the expression simplifies to: \(16y - 25\)