Problem 94 - Algebra and Trigonometry

Question

Simplify each algebraic expression. $$6-5[8-(2 y-4)]$$

Step-by-Step Solution

Answer

The simplified version of the algebraic expression is \(10y - 54\).

Step 1: Deal with Inner Parentheses

First, deal with the inner parentheses, which in this case involves simplifying the expression \(2y - 4\). Since y is a variable, this expression should remain as it is.

Step 2: Simplify Brackets

Next, replace \(2y - 4\) in the brackets, and multiply 5 by the value in the brackets, obtaining the expression: \(6 - 5[8 - (2y - 4)] = 6 - 5[8 - 2y + 4] = 6 - 5[12 - 2y]\).

Step 3: Distribute the Negative

This step involves distributing the negative sign to each term within the brackets: \(6 - 5[12 - 2y] = 6 - (60 - 10y) = 6 - 60 + 10y = -54 + 10y\).

Step 4: Reorder Expression

Finally, order the expression in descending powers of y, giving: \(-54 + 10y = 10y - 54\).