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SOLVING 1-STEP INEQUALITIES 7 th Grade Mathematics

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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.

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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

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Solving Inequalities by Addition or Subtraction Example #1: Solve n – 10 > 14. Graph the solution.

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Solving Inequalities by Addition or Subtraction Example #2: Solve y + 7 ≥ 12. Graph the solution.

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Solving Inequalities by Addition or Subtraction Example #3: Solve y + 3 < 4. Graph the solution.

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Solving Inequalities by Addition or Subtraction Example #4: Solve w + 4 ≤ -5. Graph the solution.

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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 2 6.-8 -2 4 -2 7.-8 -4 4 -4 8.-8 4 4 4

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Multiplication & Division Properties 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.

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Solving Inequalities by Multiplication or Division Example #5: Solve -3y ≤ - 27. Graph the solution.

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Solving Inequalities by Multiplication or Division Example #6: Solve 7n > -21. Graph the solution.

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Solving Inequalities by Multiplication or Division Example #7: Solve. Graph the solution.

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Solving Inequalities by Multiplication or Division Example #8: Solve. Graph the solution.

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

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Pre-Writing 1-Step Inequalities 1-Step Equations

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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.

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