Question

2x - 3 = 5 and 5x + 3 is greater than -12

Answer 1

To solve the given equations and inequality, we'll start with the equation \(2x - 3 = 5\).

### Step 1: Solve for \(x\) in the equation

1. Add 3 to both sides:
\[
2x - 3 + 3 = 5 + 3
\]
\[
2x = 8
\]

2. Divide both sides by 2:
\[
x = \frac{8}{2} = 4
\]

Thus, the solution to the equation is \(x = 4\).

### Step 2: Solve the inequality \(5x + 3 > -12\)

1. Subtract 3 from both sides:
\[
5x + 3 - 3 > -12 - 3
\]
\[
5x > -15
\]

2. Divide both sides by 5:
\[
x > -3
\]

### Conclusion

The solution to the equation \(2x - 3 = 5\) is \(x = 4\). The solution to the inequality \(5x + 3 > -12\) is \(x > -3\).

Now, to combine our findings:

- The value \(x = 4\) satisfies \(x > -3\) since \(4 > -3\).

So, the complete solution gives \(x = 4\) and \(4\) also meets the condition of the inequality.