Review of One-Step Inequalities

1. \(-2 < x \) or \(x > -2 \)

To isolate \(x\), let's divide both sides by \(9\).

\(\frac{-18}{9} < \frac{9 x}{9}\)

Now, we simplify!

• \(-2 < x \) or
  
• \(x > -2 \)
  

2. \(x \geq 33 \)

To isolate \(x\), let's add \(24\) to both sides.

\(x-24+24 \geq 9+24\)

Now, we simplify!

\(x \geq 33 \)

3. \(x \leq 120\)

To isolate \(x\), let's multiply both sides by \(-6\).

Remember that when we multiply (or divide) an inequality by a negative number, we have to flip the direction of the inequality.

\(\frac{x}{-6} \cdot-6 \leq-20 \cdot-6\)

Now, we simplify!

\(x \leq 120\)

4. \(x \geq-99\)

To isolate \(x\), let's multiply both sides by \(3\).

\(\frac{x}{3} \cdot 3 \geq-33 \cdot 3\)

Now, we simplify!

\(x \geq-99\)

5. \(x \leq 9\)

To isolate \(x\), let's add \(15\) to both sides.

\(x-15+15 \leq-6+15\)

Now, we simplify!

\(x \leq 9\)

6. \(x < \frac{3}{14}\)

To isolate \(x\), let's divide both sides by \(-14\).

Remember that when we divide (or multiply) an inequality by a negative number, we have to flip the direction of the inequality.

\(-14 x >-3\)

\(\frac{-14 x}{-14} <\frac{-3}{-14}\)

Now, we simplify!

\(x < \frac{3}{14}\)

7. \(x > 125\)

To isolate \(x\), let's multiply both sides by \(25\).

\(\frac{x}{25} \cdot 25 > 5 \cdot 25\)

Now, we simplify!

\(x > 125\)