SOLVING 1-STEP INEQUALITIES

7th Grade Mathematics

Solving 1-Step Inequalities

• When we solved 1-step equations, we did the inverse operation to both sides of the equal sign.

• When we solve 1-step inequalities, we will do the inverse operation on both sides of the inequality.

Addition & Subtraction Properties of Inequality• You can add or subtract the

same value from each side of an inequality.For addition:

• Since 7 > 3, then 7 + 4 > 3 + 4;• Therefore, if a > b, then a + c > b + c

For subtraction:• Since 6 < 9, then 6 – 3 < 9 – 3;• Therefore, if a < b, then a – c < b – c

Solving Inequalities by Addition or Subtraction

Example #1:

Solve n – 10 > 14. Graph the solution.

Solving Inequalities by Addition or SubtractionExample #2:

Solve y + 7 ≥ 12. Graph the solution.

Solving Inequalities by Addition or SubtractionExample #3:

Solve y + 3 < 4. Graph the solution.

Solving Inequalities by Addition or SubtractionExample #4:

Solve w + 4 ≤ -5. Graph the solution.

Exploration – Shoulder Partners• We can agree that -8 < 4. Work with

your partner to decide what inequality to use in each of the situations below.

1. -8 ÷ 4 4 ÷ 4

2. -8 ÷ 2 4 ÷ 2

3. -8 ÷ -2 4 ÷ -2

4. -8 ÷ -4 4 ÷ -4

5. -8 2 4 26. -8 -2 4 -27. -8 -4 4 -4

8. -8 4 4 4

Multiplication & DivisionProperties of Inequality• If you multiply or divide each side

of an inequality by the same positive number, the direction of the inequality remains unchanged.

• If you multiply or divide each side of an inequality by the same negative number, the direction of the inequality is reversed.

Solving Inequalities by Multiplication or Division

Example #5:

Solve -3y ≤ - 27. Graph the solution.

Solving Inequalities by Multiplication or Division

Example #6:

Solve 7n > -21. Graph the solution.

Solving Inequalities by Multiplication or Division

Example #7:

Solve . Graph the solution.

Solving Inequalities by Multiplication or Division

Example #8:

Solve . Graph the solution.

Writing in Math

• Write a paragraph describing 3 similarities and 2 differences in solving 1-step equations & 1-step inequalities.

Pre-Writing

Writing a Paragraph…There are many important similarities and differences in solving 1-step equations and inequalities. One similarity is _____________________________________________________________________________________ Another thing solving equations and inequalities have in common is ______________ ____________________________________________________ A third similarity is ________________________________________________________________________________________There are also important differences between solving equations and inequalities. One difference is________________________ ____________________________________________________ Another important difference to remember is that___________ ____________________________________________________While solving 1-step inequalities have many things in common, there are also many important differences.