Question

What is the algebraic expression for "half of a number increases by 9" which is equal to 54?

A) (x/2) + 9 = 54
B) (x/2) - 9 = 54
C) (x/2) + 9 = 54x
D) (x/2) - 9 = 54x

Answer 1

The algebraic expression for "half of a number increases by 9" equal to 54 is (x/2) + 9 = 54. Through a series of algebraic steps, we solve for x, arriving at x = 90.

Step-by-step explanation:

The correct algebraic expression for the phrase "half of a number increases by 9" which is equal to 54 is (x/2) + 9 = 54. This equation can be solved to find the value of x.

Let's solve this step-by-step:

1. Subtract 9 from both sides of the equation to isolate the term involving x: (x/2) = 54 - 9.
2. Calculate the right side of the equation: (x/2) = 45.
3. Multiply both sides by 2 to solve for x: x = 45 * 2.
4. The number x is therefore 90.

The student should understand that when creating algebraic expressions, converting phrases into mathematical operations is essential. In this case, "half of a number" translates to (x/2), and "increases by 9" translates to adding 9 to the expression.