Question

Determine which of the following equations have a solution of 𝑝=8. Select all that apply.
*
1 point
24 = 6(p-4)
2p - 1 = 17
1/2P = -4
3p + 5 + 13 + 2p

Answer 1

To determine which of the following equations have a solution of \( p = 8 \), we will substitute \( p = 8 \) into each equation and see if they hold true.

1. **Equation:** \( 24 = 6(p - 4) \)

Substitute \( p = 8 \):
\[
24 = 6(8 - 4)
\]
\[
24 = 6 \times 4
\]
\[
24 = 24 \quad \text{(True)}
\]

2. **Equation:** \( 2p - 1 = 17 \)

Substitute \( p = 8 \):
\[
2(8) - 1 = 17
\]
\[
16 - 1 = 17
\]
\[
15 = 17 \quad \text{(False)}
\]

3. **Equation:** \( \frac{1}{2}p = -4 \)

Substitute \( p = 8 \):
\[
\frac{1}{2}(8) = -4
\]
\[
4 = -4 \quad \text{(False)}
\]

4. **Equation:** \( 3p + 5 + 13 + 2p = ? \) (need an expression for comparison)

First, simplify the left side:
\[
3p + 2p + 5 + 13 = 5p + 18
\]

Now substitute \( p = 8 \):
\[
5(8) + 18 = ?
\]
\[
40 + 18 = 58
\]

This doesn't directly equal anything, so it's unclear if this has a specific equality. However, since there's no equality presented, it can't confirm \( p = 8 \) is a solution.

**Final results:**
The only equation that has a solution of \( p = 8 \) is:

- \( 24 = 6(p - 4) \) **(True)**

The other equations do not hold true. The last equation is ambiguous without an equality. Thus the valid one is the first equation.