# Chapter 7 Lesson 4 Solving Inequalities by Adding or Subtracting pgs. 345-349 What you’ll learn: Solve inequalities by using the Addition or Subtraction.

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Chapter 7 Lesson 4 Solving Inequalities by Adding or Subtracting pgs. 345-349 What you’ll learn: Solve inequalities by using the Addition or Subtraction Properties of Inequality What you’ll learn: Solve inequalities by using the Addition or Subtraction Properties of Inequality

k Solving an inequality means finding values for the variable that make the inequality true. k You can solve inequalities by using the Addition and Subtraction Properties of Inequalities (pg. 345) This is the same concept as using the Addition/Subtraction Properties of Equations (Lesson 3-3 pgs. 110-111) k Solving an inequality means finding values for the variable that make the inequality true. k You can solve inequalities by using the Addition and Subtraction Properties of Inequalities (pg. 345) This is the same concept as using the Addition/Subtraction Properties of Equations (Lesson 3-3 pgs. 110-111)

Example 1: Solving an Inequality using Subtraction Solve -13  9 + b Check your solution Write the inequality: -13  9 + b Subtract 9 from each side: -13  9 + b -9 -9 Simplify: -22  b or b  -22 To check your solution, try any number less than or equal to -22 Check using -22: -13  9 + (-22) -13  -13  Check: using -30 -13  9 + -30 -13  -21  Check using -20: -13  9 + -20 -13  -11

Example 2: Solving an Inequality using Addition Solve a - 5  6 Check your solution Write the inequality: a - 5  6 Add 5 to both sides: a - 5  6 +5 +5 Simplify: a  11 Check your result by using any number greater than 11 Check using 12: 12 - 5  6 7  6  Check using 32: 32 - 5  6 27  6  Check using 7: 7 - 5  6 2  6

Example 3: Graph Solutions of Inequalities Solve h + 4  4 Then graph the solution on a number line. Write the inequality: h + 4  4 Subtract 4 from each side: h + 4  0 - 4 -4 h  0 The solution is h  0 Check: any number greater than 0 I’m using 1 1 + 4  4 5  4  Now graph the solution On a number line. Done on board in class.

Example 4: Use an Inequality to Solve a Problem Chris is saving money for a ski trip. He has \$62.50, but his goal is to save at least \$100. What is the least amount Chris needs to save to reach his goal? Explore: We need to find the least amount Chris needs to save Plan: Let x represent the amount he needs to save. Write an inequality to represent the problem. Remember at least means greater than or equal to. x + 62.50  100 Solve: x + 62.50  100 - 62.50 -62.50 x  37.50 So the least amount that Chris needs to save is \$37.50

Your Turn! Solve the inequality, graph your solution, do a check A.c - (-2)  3 B.25  n + (-12) C.g - 1  2 D.k + 9  -21 A.c - (-2)  3 B.25  n + (-12) C.g - 1  2 D.k + 9  -21 2 3 1616 c + 2  3 Check using -1 -2 -2 -1 - (-2)  3 c  1 1  3  25  n + (-12) Check using 40 +12 +12 25  40 + (-12) 37 < n, n  37 25  28  g - 5 + 5  13 + 5 Check using 4 3 3 6 3 4 - 1  2 g  3 2  2  2323 1616 1313 1616 k + 9  -21 Check using -25 - 9 -9 -25 + 9  -30 k  -30 -16  -30  5656

kExtra Practice by the door on your way out. See me if you have questions/problems!

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