Question

which description represents an expression? what is the difference between expressions and equations? equations have _____ signs and expressions do not. write each answer choice in number form. a. a number to the fifth power is thirty-two b. a number times eight is forty-eight c. five is greater than a number divided by two d. six and seventy-five hundredths times a number plus three the correct answer is _ because the wording (the word ____) shows a solution to the problem.

Explanation:

Step1: Define expressions vs equations

Equations contain equality/inequality signs; expressions do not.

Step2: Translate each option to number form

Option A:

Let the number be $x$.
$x^5 = 32$ (has equality sign: equation)

Option B:

Let the number be $x$.
$8x = 48$ (has equality sign: equation)

Option C:

Let the number be $x$.
$5 > \frac{x}{2}$ (has inequality sign: equation)

Option D:

Let the number be $x$.
$6.75x + 3$ (no equality/inequality sign: expression)

Step3: Identify the expression

Only Option D is an expression, as it lacks a relational sign. The key wording is the absence of a verb like "is" or "greater than" that indicates a relational sign.

Answer:

D. Six and seventy-five hundredths times a number plus three
because the wording (the lack of a relational verb like "is") shows it is an expression, not an equation.