\(\displaystyle -x+16< 24\) Subtract \(\displaystyle 16\) on both sides.

\(\displaystyle -x< 8\) Divide \(\displaystyle -1\) on both sides. When dividing with a negative number, our answer is negative. Also, we must FLIP the inequality.

\(\displaystyle x>-8\)

\(\displaystyle -3x+17>-13\) Subtract \(\displaystyle 17\) on both sides. When adding with another negative number, we just add the numbers and put a minus sign in front.

\(\displaystyle -3x>-30\) Divide \(\displaystyle -3\) on both sides. When dividing with another negative number, our answer is positive. Also, FLIP the sign. 

\(\displaystyle x< 10\)

\(\displaystyle \frac{3}{2}x\geq12\) Multiply \(\displaystyle \frac{2}{3}\) on both sides.

\(\displaystyle x\geq8\)

\(\displaystyle -3x\leq-27\) Divide \(\displaystyle -3\) on both sides. When dividing with another negative number, our answer is positive. We also need to FLIP the inequality sign.

\(\displaystyle x\geq9\)

\(\displaystyle -\frac{x}{2}< 4\) Multiply \(\displaystyle 2\) on both sides. Remember to FLIP the inequality.

\(\displaystyle x>-8\)

\(\displaystyle -\frac{3x}{5}-15< 12\) Add \(\displaystyle 15\) on both sides.

\(\displaystyle -\frac{3x}{5}< 27\) Multiply \(\displaystyle \frac{5}{3}\) on both sides. Remember to FLIP the inequality sign. If you try to multiply both sides by \(\displaystyle -\frac{5}{3}\), you will have the wrong answer. When dealing with inequality equations, always multiply or divide the positive number in front of the variable.

\(\displaystyle x>-45\)

\(\displaystyle -3(x+1)\leq21\) Distribute. If you decide to divide both sides by \(\displaystyle -3\), you will change the answer. When dealing with inequalities, distribute first. 

\(\displaystyle -3x-3\leq21\) Add \(\displaystyle 3\) on both sides.

\(\displaystyle -3x\leq24\) Divide \(\displaystyle -3\) on both sides. Remember to FLIP the inequality sign.

\(\displaystyle x\geq-8\)

\(\displaystyle x^2\leq 9\) Anytime you exponents in inequalities, you need to think of ranges of values that are acceptable. Remember, when an exponent is squared, negative values are also acceptable since two negatives multiplied are positive. We take the square root of both sides.

\(\displaystyle x= \pm3\) Now, we need to know how to make the range for \(\displaystyle x\). We know if \(\displaystyle x\) is \(\displaystyle \pm2\), this will satisfy the inequality since \(\displaystyle 4\) is less than \(\displaystyle 9\). Also, \(\displaystyle \pm2\) is between \(\displaystyle -3, 3\). Our final answer is \(\displaystyle -3\leq x \leq3\).

\(\displaystyle x^2> 9\) Anytime you exponents in inequalities, you need to think of ranges of values that are acceptable. Remember, when an exponent is squared, negative values are also acceptable since two negatives multiplied are positive. We take the square root of both sides.

\(\displaystyle x= \pm3\) Now, we need to know how to make the range for \(\displaystyle x\). We know if \(\displaystyle x\) is \(\displaystyle \pm4\), this will satisfy the inequality since \(\displaystyle 16\) is greater than \(\displaystyle 9\). So then we know \(\displaystyle 4>3\) and \(\displaystyle -3>-4\). Our final answer is \(\displaystyle x>3\) or \(\displaystyle x< -3\).

Solve the way you would solve an equation. First add 7 to both sides 

\(\displaystyle 2x \leq 8\) now divide both sides by 2 

\(\displaystyle x \leq 4\)