Question

Which equation matches the solution set of five x squared minus 10 equals 15 3x / 5 + 4 = 7 2x - 20 + 30 x + x - 9 = 1 + x

Answer 1

Let's solve each equation one by one to find the solution sets.

1. **Equation 1**: \(5x^2 - 10 = 15\)

Start by adding 10 to both sides:

\[
5x^2 = 25
\]

Divide both sides by 5:

\[
x^2 = 5
\]

Taking the square root of both sides, we get:

\[
x = \sqrt{5} \quad \text{or} \quad x = -\sqrt{5}
\]

So the solution set is \( \{ -\sqrt{5}, \sqrt{5} \} \).

2. **Equation 2**: \(\frac{3x}{5} + 4 = 7\)

Subtract 4 from both sides:

\[
\frac{3x}{5} = 3
\]

Multiply both sides by 5:

\[
3x = 15
\]

Divide by 3:

\[
x = 5
\]

So the solution set is \( \{ 5 \} \).

3. **Equation 3**: \(2x - 20 + 30x + x - 9 = 1 + x\)

Combine like terms on the left side:

\[
(2x + 30x + x - x) - 20 - 9 = 1
\]

Simplify:

\[
32x - 29 = 1
\]

Add 29 to both sides:

\[
32x = 30
\]

Divide by 32:

\[
x = \frac{30}{32} = \frac{15}{16}
\]

So the solution set is \( \{ \frac{15}{16} \} \).

Now let’s summarize the solution sets:

1. For \(5x^2 - 10 = 15\), the solution set is \( \{ -\sqrt{5}, \sqrt{5} \} \).
2. For \(\frac{3x}{5} + 4 = 7\), the solution set is \( \{ 5 \} \).
3. For \(2x - 20 + 30x + x - 9 = 1 + x\), the solution set is \( \{ \frac{15}{16} \} \).

Please clarify if you are looking for something specific with these equations or if you wish to compare the solution sets.