Problem 9 - College Algebra Essentials

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 algebraic expression \(4+5(x-7)^{3}\) for \(x = 9\) evaluates to 44.

Step 1: Substitute the Value

Substitute the given value of x (which is 9) in the expression. Here, \(x = 9\), so the equation becomes \(4 + 5(9 - 7)^3\).

Step 2: Simplify within the Brackets

Calculate the operation within the brackets first as per the order of operations (2). Hence, the equation becomes \(4+ 5(2)^3\).

Step 3: Evaluate the Exponential

Evaluate the exponent next as per the order of operations. \(2^3\) implies \(2*2*2\) which equals 8. So, the equation becomes \(4 + 5*8\).

Step 4: Evaluate the Multiplication

Now, as per the order of operations, multiply 5 with 8, resulting in 40. So, the equation becomes \(4 + 40\).

Step 5: Evaluate the Addition

Add 4 and 40 to get the final result. Here, \(4 + 40 = 44\).