Practice Solving One-Step Inequalities

Solve for $$x$$

Your answer must be simplifies

1. $$-18 < 9x$$

2. $$-4+x\leq9$$

3. $$-7x > 10$$

4. $$\dfrac x 7\geq-6$$

5. $$-3 < x-10$$

6. $$-x < -29$$

7. $$7 > \dfrac x4$$

Source: Khan Academy, https://www.khanacademy.org/math/algebra-basics/alg-basics-linear-equations-and-inequalities/alg-basics-one-step-inequalities/e/one_step_inequalities
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1. To isolate ‍$$x$$, let's divide both sides by ‍9.

   $$\dfrac{-18}{9} < \dfrac{9x}{9}$$

   Now, we simplify!

   $$-2 <  x$$ or $$x > -2$$

2. To isolate ‍$$x$$, let's subtract -4 from both sides.

   $$-4-(-4)+x\leq9-(-4)$$

   Now, we simplify!

   $$x\leq13$$

3. To isolate ‍$$x$$, let's divide both sides by ‍-7.

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

   $$\begin{aligned}
   -7x& > 10\\\\
   \dfrac{-7x}{-7}& < \dfrac{10}{-7}
   \end{aligned}$$

   Now, we simplify!

   $$ x < - \dfrac{10}{7} $$

4. To isolate ‍$$x$$, let's multiply both sides by ‍7.

   $$\dfrac x 7\cdot7\geq-6\cdot7$$

   Now, we simplify!

   $$x\geq-42$$

5. To isolate ‍$$x$$, let's add 10 to both sides.

   $$-3+10 < x-10+10$$

   Now, we simplify!

   $$7 < x$$ or $$x > 7$$

6. To isolate ‍$$x$$, let's divide both sides by ‍-1.
   
   Remember that when we divide (or multiply) an inequality by a negative number, we have to flip the direction of the inequality.

   $$\begin{aligned}
   -x& < -29\\\\
   \dfrac{-x}{-1}& > \dfrac{-29}{-1}
   \end{aligned}$$

   Now, we simplify!

   $$x > 29$$

7. To isolate ‍$$x$$, let's multiply both sides by ‍4.

   $$7\cdot4>\dfrac{x}{4}\cdot4$$

   Now, we simplify!

   $$28 > x$$ or $$x < 28$$