To find the solution set of the equations $2x - 3 = 5$ and the inequality $5x + 3 -12$, we will solve each one separately and then find the intersection of their solutions.

Question

To find the solution set of the equations $2x - 3 = 5$ and the inequality $5x + 3 > -12$, we will solve each one separately and then find the intersection of their solutions.
1. **Solve the equation $2x - 3 = 5$**:

$$
2x - 3 = 5
$$
Add 3 to both sides:
$$
2x = 5 + 3
$$
$$
2x = 8
$$
Divide by 2:
$$
x = 4
$$

2. **Solve the inequality $5x + 3 > -12$**:

$$
5x + 3 > -12
$$
Subtract 3 from both sides:
$$
5x > -12 - 3
$$
$$
5x > -15
$$
Divide by 5 (and since 5 is a positive number, the inequality remains the same):
$$
x > -3
$$

3. **Combine the solutions**:

The solution to the equation $2x - 3 = 5$ gives us $x = 4$.
The solution to the inequality $5x + 3 > -12$ gives us $x > -3$.

Since $x = 4$ satisfies $x > -3$, the combined solution set is simply $x = 4$.

**Final Answer**: The solution set is $\{4\}$.

make this wayyyy smaller

GPT-4o mini · Answer

To solve the equations $2x - 3 = 5$ and $5x + 3 > -12$: 1. **Solve the equation**: $$ 2x - 3 = 5 \implies 2x = 8 \implies x = 4 $$ 2. **Solve the inequality**: $$ 5x + 3 > -12 \implies 5x > -15 \implies x > -3 $$ 3. **Combine the solutions**: The solution $x = 4$ satisfies the inequality $x > -3$. **Final Answer**: The solution set is $\{4\}$.

To find the solution set of the equations \(2x - 3 = 5\) and the inequality \(5x + 3 > -12\), we will solve each one separately and then find the intersection of their solutions.