Let's solve the inequalities one by one.
-
Solve the inequality \(4x - 3 < 9\): \[ 4x - 3 < 9 \] Add 3 to both sides: \[ 4x < 12 \] Divide both sides by 4: \[ x < 3 \]
-
Solve the inequality \(x + 6 > -2\): \[ x + 6 > -2 \] Subtract 6 from both sides: \[ x > -8 \]
Now, we combine the results from both inequalities:
- From \(4x - 3 < 9\), we have \(x < 3\).
- From \(x + 6 > -2\), we have \(x > -8\).
Thus, the solution set is: \[ -8 < x < 3 \]
In interval notation, the solution set is: \[ (-8, 3) \]