Question

ook 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 solve the equation \(-15x = 24 + 16x = 3x - 24\) and transform it into the form \(x = a\), where \(a\) is a number, let's first clarify the equation. It appears to be a compound equation, so we should treat it as two separate equations:

1. \(-15x = 24 + 16x\)
2. \(-15x = 3x - 24\)

Let's focus on the first equation \(-15x = 24 + 16x\).

From this equation, we can apply the following transformations:

1. **B**: Subtract \(16x\) from both sides:
\[
-15x - 16x = 24 \implies -31x = 24.
\]
Then, simplifying gives:
\[
x = -\frac{24}{31}.
\]

Next, let’s look at the second equation \(-15x = 3x - 24\).

2. **D**: Add \(15x\) to both sides:
\[
0 = 18x - 24 \implies 18x = 24,
\]
then simplifying gives:
\[
x = \frac{24}{18} = \frac{4}{3}.
\]

Both approaches indicate that we can manipulate the equation toward a single solution for \(x\).

The correct options that apply are:

- **B**: Subtract 15x from both sides of the equation and then simplify (to isolate \(x\)).
- **D**: Add 3x to both sides of the equation and then simplify (to also isolate \(x\)).

In summary, the two steps that can be taken to simplify into the form \(x = a\) are **B** and **D**.