Problem 93 - Algebra and Trigonometry

Question

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

Step-by-Step Solution

Answer

The simplified algebraic expression is \(16y - 25\).

Step 1: Distribute the Inner Parentheses

To start, distribute the -4 into the parentheses \(3 - (4y - 5)\). This becomes \(7 - 4 * 3 + 4 * (4y - 5)\). Carefully watch the signs. The -4 multiplies both 3 and the quantity (4y - 5), turning the subtraction to addition due to the negative sign.

Step 2: Perform the Multiplication

Now perform the multiplication operation, \(7 - 12 + 16y - 20\). This resulted from multiplying -4 by 3 and 4 by 4y and -5 respectively.

Step 3: Combine Like Terms

Then combine like terms to simplify the expression: \(16y + 7 - 12 - 20 = 16y - 25\).