Question

Look at the equation shown.
-15x + 24 + 16x = 3x - 24
What is a step that can be used to transform the equation into the form x = a, where a 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 the form \(x = a\), where \(a\) is a number, we can follow these steps. The goal is to first simplify and combine terms.

Looking at the options provided, the best choices to move towards solving for \(x\) are:

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

This will help to combine the \(x\) terms on one side, giving:
\[
-15x + 16x + 24 = 3x - 24 \implies x + 24 = 3x - 24
\]

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

This will also help facilitate combining the \(x\) terms:
\[
-15x + 16x + 24 = 3x - 24 \implies -15x + 24 = -24 \implies 24 = 3x + 15x - 24
\]

After performing either of these operations, we would then simplify the equation appropriately and isolate \(x\) to solve for it.

Thus, the two options that can be selected to transform the equation into the desired form are:
- **B** (subtract 15x from both sides and simplify)
- **D** (add 3x to both sides and simplify)