We are given two inequalities to solve for $x$:

1. $5x - 2 > -42$
2. $5x - 2 < 43$

Solving the first inequality:

$5x - 2 > -42$ Add 2 to both sides: $5x > -40$ Now, divide both sides by 5: $x > -8$

Solving the second inequality:

$5x - 2 < 43$ Add 2 to both sides: $5x < 45$ Now, divide both sides by 5: $x < 9$

Combined result:

The solution is: $-8 < x < 9$ This means $x$ is greater than $-8$ and less than $9$.

Would you like more details or have any questions?

Related questions:

1. How would the solution change if the inequality symbols were reversed?
2. How do you graph the solution on a number line?
3. What happens if there are different coefficients for $x$ in each inequality?
4. How would the solution change if it were a compound inequality with "and" instead of "or"?
5. Can you solve similar inequalities with absolute values?

Tip:

When solving inequalities, remember that multiplying or dividing by a negative number reverses the inequality sign.