Question

Select the correct expressions in the table.
Select all the expressions that are equivalent to -6(3x - 7).

-18x - 7 4 - 10(3x - 7)
4(3x + 5) - 2(15x - 11) 6(3x + 7)
2x - 7 - 5(4x - 7) -2(9x - 21)

Answer 1

To determine which expressions are equivalent to \(-6(3x - 7)\), we first simplify that expression:

\[
-6(3x - 7) = -6 \cdot 3x + 6 \cdot 7 = -18x + 42.
\]

Now we will simplify each expression in the table to see which ones are equivalent to \(-18x + 42\).

1. **\(-18x - 7\)**:
\[
-18x - 7 \quad (\text{Not equivalent because it lacks the } +42)
\]

2. **\(4 - 10(3x - 7)\)**:
\[
4 - 10(3x - 7) = 4 - 30x + 70 = -30x + 74 \quad (\text{Not equivalent})
\]

3. **\(4(3x + 5) - 2(15x - 11)\)**:
\[
4(3x + 5) - 2(15x - 11) = (12x + 20) - (30x - 22) = 12x + 20 - 30x + 22 = -18x + 42 \quad (\text{Equivalent})
\]

4. **\(6(3x + 7)\)**:
\[
6(3x + 7) = 18x + 42 \quad (\text{Not equivalent})
\]

5. **\(2x - 7 - 5(4x - 7)\)**:
\[
2x - 7 - 5(4x - 7) = 2x - 7 - 20x + 35 = -18x + 28 \quad (\text{Not equivalent})
\]

6. **\(-2(9x - 21)\)**:
\[
-2(9x - 21) = -18x + 42 \quad (\text{Equivalent})
\]

Now, compiling the results, the expressions that are equivalent to \(-6(3x - 7)\) are:

- \(4(3x + 5) - 2(15x - 11)\)
- \(-2(9x - 21)\)

Thus, the equivalent expressions are:

- **\(4(3x + 5) - 2(15x - 11)\)**
- **\(-2(9x - 21)\)**