Question

-15x + 24 + 16x = 3x - 24
What is a step that can be used to transform the equation into the form, where
is a number, to show that the equation has one solution? Select two options that apply.

A.
combine like terms 15x and 16x to get 31x and then subtract 31x from both sides of the equation

B.
subtract 15x from both sides of the equation and then simplify

C.
subtract 24 from both sides of the equation and then simplify

D.
add 3x to both sides of the equation and then simplify

E.
add 24 to both sides of the equation and then simplify

Answer 1

To transform the equation \(-15x + 24 + 16x = 3x - 24\) into a form that shows it has one solution, we need to simplify and combine like terms. Here are the appropriate steps to take:

1. **Combine like terms**: In the expression \(-15x + 16x\), we can combine these terms to simplify the left side of the equation.
2. **Isolate the variable**: After simplification, you will want to isolate \(x\) on one side to clearly see that there is one solution.

From the provided options, the two steps that apply are:

**B.** subtract 15x from both sides of the equation and then simplify
**D.** add 3x to both sides of the equation and then simplify

Both of these steps will help simplify the equation correctly and lead towards isolating \(x\). After performing these operations, you will find that \(x\) can be expressed as a number, indicating that the equation has one solution.