Problem 10 - Algebra and Trigonometry

Question

Evaluate each algebraic expression for the given value or values of the variable(s). $$6+5(x-6)^{3}, \text { for } x=8$$

Step-by-Step Solution

Answer

The evaluated value of the algebraic expression when \(x = 8\) is 46.

Step 1: Substitution

Replace \(x\) with 8 in the original expression, giving \(6 + 5(8-6)^{3}\).

Step 2: Simplify the Bracket

Simplify the expression inside the bracket, giving \(6 + 5(2)^{3}\).

Step 3: Simplify the Power

The third power of 2 is 8, so the expression becomes \(6 + 5*8\).

Step 4: Multiply

Multiplying 5 by 8 gives 40, so the expression becomes \(6 + 40\).

Step 5: Addition

Adding 6 to 40 gives 46.