Problem 94 - College Algebra Essentials

Question

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

Step-by-Step Solution

Answer

The simplified form of the given algebraic expression is \(-54 + 10y\).

Step 1: Simplify the Innermost Brackets

Start with the expression inside the innermost brackets i.e. \(2 y - 4\). There is nothing to simplify here as the expression consists of different terms.

Step 2: Simplify the Outer Brackets

In the second brackets, subtract the expression of step1 from 8, i.e. \(8 - (2 y - 4)\). This simplifies to \(8 - 2y + 4 = 12 - 2y\). So the original expression becomes \(6 - 5*(12 - 2y)\).

Step 3: Distribute the Multiplication

Handle the multiplication next. Multiply 5 with each term inside the bracket. Thus, the expression becomes \(6 - 5*12 + 5*2y = 6 - 60 + 10y\).

Step 4: Perform the Summation

Lastly, perform the summation. The term \(6 - 60\) results in \(-54\) and the final simplified expression becomes \(-54 + 10y\).