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 \(x < 28\)