Review of One-Step Inequalities

1. Solve for $x$.
Your answer must be simplified.

$-18 < 9 x$

2. Solve for $x$.
Your answer must be simplified.

$x-24 \geq 9$

3. Solve for $x$.
Your answer must be simplified.

$\frac{x}{-6} \geq-20$

4. Solve for $x$.
Your answer must be simplified.

$\frac{x}{3} \geq-33$

5. Solve for $x$.
Your answer must be simplified.

$x-15 \leq-6$

6. Solve for $x$.
Your answer must be simplified.

$-14 x >-3$

7. Solve for $x$.
Your answer must be simplified.

$\frac{x}{25} > 5$

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.

$-14 x >-3$

$\frac{-14 x}{-14}$

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!

$x > 125$