Problem 9 - Algebra and Trigonometry

Question

Evaluate each algebraic expression for the given value or values of the variable(s). $$4+5(x-7)^{3}, \text { for } x=9$$

Step-by-Step Solution

Answer

The evaluation of the algebraic expression \(4+5(x-7)^{3}\) for \(x=9\) is 44

Step 1: Substitute the value

Substitute \(x=9\) into the given algebraic expression. So, our equation becomes \(4+5(9-7)^{3}\)

Step 2: Simplify inside the Bracket

Calculate the expression inside the bracket first. So, the expression becomes \(4+5(2)^{3}\)

Step 3: Evaluate exponentiation

Next, calculate the exponentiation, which is \(2^{3}=8\). So, the expression becomes \(4+5(8)\)

Step 4: Multiply

Perform multiplication next. \(5*8=40\). So, the expression becomes \(4+40\)

Step 5: Perform Addition

Finally, complete by adding 4 and 40 to get 44