Question

Which expressions are equivalent to 5 x minus 15? Select three options.
5 (x + 15)
5 (x minus 3)
4 x + 3 y minus 15 minus 3 y + x
Negative 7 y minus 6 x minus 8 y + x
Negative 20 minus 3 x + 5 + 8 x

Answer 1

To find expressions equivalent to \(5x - 15\), we can simplify each option. Let's analyze them one by one:

1. **\(5 (x + 15)\)**:
\[
5(x + 15) = 5x + 75 \quad (\text{not equivalent})
\]

2. **\(5 (x - 3)\)**:
\[
5(x - 3) = 5x - 15 \quad (\text{equivalent})
\]

3. **\(4x + 3y - 15 - 3y + x\)**:
Simplifying the expression:
\[
4x + 3y - 3y - 15 + x = 4x + x - 15 = 5x - 15 \quad (\text{equivalent})
\]

4. **\(-7y - 6x - 8y + x\)**:
Simplifying this expression:
\[
-7y - 8y - 6x + x = -15y - 5x \quad (\text{not equivalent})
\]

5. **\(-20 - 3x + 5 + 8x\)**:
Simplifying this expression:
\[
-20 + 5 + 8x - 3x = -15 + 5x \quad (\text{not equivalent})
\]

The equivalent expressions to \(5x - 15\) are:
- \(5(x - 3)\)
- \(4x + 3y - 15 - 3y + x\)

So the three options that are equivalent to \(5x - 15\) are:
1. \(5 (x - 3)\)
2. \(4x + 3y - 15 - 3y + x\)

Since we only found two so far, I must clarify that we only found **two** expressions from the provided list. Please check if there are more options or if any were mislisted. The correct answers are:
- \(5 (x - 3)\)
- \(4x + 3y - 15 - 3y + x\)