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Chapter 0: Problem 93

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

Short Answer

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

Step by step solution

01

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.
02

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: \(7 - 12 + 16y - 20\).
03

Combine 'Like' Terms

Simplify by gathering the 'y' terms and the constants separately. The expression becomes: \(16y + 7 -12 -20\).
04

Simplify the Expression

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

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