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Chapter 0: Problem 9

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

Short Answer

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

Step by step solution

01

Substitute the Value

Substitute the given value of x (which is 9) in the expression. Here, \(x = 9\), so the equation becomes \(4 + 5(9 - 7)^3\).
02

Simplify within the Brackets

Calculate the operation within the brackets first as per the order of operations (2). Hence, the equation becomes \(4+ 5(2)^3\).
03

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 \(4 + 5*8\).
04

Evaluate the Multiplication

Now, as per the order of operations, multiply 5 with 8, resulting in 40. So, the equation becomes \(4 + 40\).
05

Evaluate the Addition

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

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