What is the solution set of 2x - 3 = 5 and 5x + 3 > -12?

Answer 1

To find the solution set for the equations and inequality given, we can solve them step by step.

1. Solve the equation: \[ 2x - 3 = 5 \] Add 3 to both sides: \[ 2x = 8 \] Now, divide by 2: \[ x = 4 \]

2. Solve the inequality: \[ 5x + 3 > -12 \] Subtract 3 from both sides: \[ 5x > -15 \] Now, divide by 5: \[ x > -3 \]

Now we combine the results:

• From the equation, we found \( x = 4 \).
• From the inequality, we found \( x > -3 \).

The solution set must satisfy both conditions. Since \( x = 4 \) is greater than \(-3\), it satisfies the inequality.

Final Solution Set: The solution set is \({4}\) because it is the value of \( x \) which satisfies both the equation and the inequality.