Problem 10 - College Algebra Essentials

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 value of the algebraic expression \(6+5(x-6)^{3}\) for \(x=8\) is 46.

Step 1: Substitution

Substitute 8 for x in the given expression. This will give us \( 6+5(8-6)^3 \).

Step 2: Simplification

Simplify the expression inside the brackets first as per the order of operations(BODMAS/BIDMAS), which states that the operation of brackets should be done first. This gives us \( 6+5(2)^3 \). After this, continue simplifying the expression by cubing the number inside the brackets, \(2^{3}\) equals 8. This provides you with the new expression, \(6+5*8 \).

Step 3: Final Calculation

Now we can perform the multiplication, \(5*8\) equals 40. And finish the calculation by adding 6 + 40 to get the final result.