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More Lessons for Grade 8 Math
Math Worksheets
Videos, worksheets, stories and songs to help Grade 8 students learn about solving one-step linear inequalities by multiplication or division.
One-step linear inequalities are solved using addition, subtraction, multiplication, or division, similar to equations. However, there’s one critical rule:
When multiplying or dividing by a negative number, flip the inequality sign.
The inequality sign does not change when adding or subtracting.
The solutions to linear inequalities can be expressed in several ways: using inequalities, using a graph, or using interval notation.
The following diagrams give examples of solving a one-step linear inequalities. Scroll down the page for more examples and solutions.
Algebra Worksheets
Practice your skills with the following Algebra worksheets:
Printable & Online Algebra Worksheets
Example 1: Using Addition
Solve: x − 7 < 10
Add 7 to both sides.
x − 7 + 7 < 10 + 7
Solution: x < 17
Example 2: Using Subtraction
Solve: y + 3 ≥ 5
Subtract 3 from both sides.
y + 3 − 3 ≥ 5 − 3
Solution: y ≥ 2
Example 3: Multiplying by a Positive Number
Solve: \(\frac{w}{2} \le 4 \)
Multiply both sides by 2.
\(\frac{w}{2} × 2 ≤ 4 × 2 \)
Solution: w ≤ 8
Example 4: Dividing by a Positive Number
Solve: 5z > 20
Divide both sides by 5.
\(\frac{5z}{5} > \frac{20}{5} \)
Solution: z > 4
Multiplying/Dividing by a Negative Number
Multiplying or dividing both sides of an inequality by a negative number MUST reverse the direction of the inequality symbol.
Example 5: Multiplying by a Negative Number
Solve: \(\frac{a}{-3} < 6 \)
Multiply both sides by -3 (which is negative).
\(\frac{a}{-3} × (−3) > 6 × (−3) \) <– Remember to flip the symbol
Solution: a > −18
Example 6: Dividing by a Negative Number
Solve: −4b ≤ 12
Divide both sides by -4 (which is negative).
\(\frac{-4b}{-4} × (−4) ≥ 12 ×(−4) \) <– Remember to flip the symbol
Solution: b ≥ −3
One-Step Inequalities
One-Step Inequalities 2
One-step Inequality Examples
Solving one-step inequalities
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