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Solving Inequalities: Addition, Subtraction, and Graphing on a Number Line

This educational resource focuses on solving inequalities using addition and subtraction, as well as graphing them on a number line. It introduces students to the concepts of open and closed dots, set notation, and graphical representations. Through examples and exercises, learners will explore how to solve inequalities like (x < 3), (y geq -5/4), and (p <br>eq 2). The guide includes step-by-step methods for simplifying inequalities, checking solutions, and understanding the graphical outcomes. Ideal for high school mathematics.

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Solving Inequalities: Addition, Subtraction, and Graphing on a Number Line

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  1. 6.1 Solving Inequalities with adding and subtracting • graph inequalities on a number line. • solve inequalities using addition and subtraction. SOL: A.1, A.3 Designed by Skip Tyler, Varina High School Edited by Eddie Judd, Crestwood Middle School

  2. o 1) Graph the solution set ofx < 3. When you have < or >, use an open dot!

  3. • 2) Graph the solution set ofy ≥ -5/4. When you have ≤ or ≥, use a closed dot! Converting -5/4 to a decimal = -1.25

  4. o 3) Graph the solution set ofp ≠ 2. When you have ≠, use an open dot and shade both ways!

  5. Answer Now 4) Which inequality would have a closed dot on the number line? • > • < • ≥ • ≠

  6. Answer Now 5) Which inequality does NOT use an open dot on the number line? • ≤ • < • > • ≠

  7. o 29 30 31 6) Solve x + (-14) < 16 • Solve this problem like an equation • Draw “the river” • Eliminate double signs • Add 14 to both sides • Simplify Set Notation • Check your limit • Graph the solution x- 14< 16 + 14 + 14 {x|x < 30} 30 + (-14) = 16 16 = 16

  8. ● -15 -14 -13 7) Solve y + 21 ≥ 7 • Draw the “river” • Subtract 21 from both sides • Simplify in Set Notation • Check your limit • Graph the solution - 21 -21 {y|y≥ -14} (-14) + 21 = 7 7 = 7

  9. o 16 17 18 8) Solve 8y + 3 > 9y - 14 - 8y - 8y 3 > y - 14 + 14 + 14 17 > y {y|y < 17} 8(17) + 3 = 9(17) - 14 • Draw “the river” • Subtract 8y from both sides • Simplify • Add 14 to both sides • Simplify • Rewrite inequality in Set Notation • Check your limit • Graph the solution

  10. o 6 7 8 o 6 7 8 ● 6 7 8 6 7 8 Answer Now 9) What is the graph of 7 ≤ m? ●

  11. ● 30 31 32 - 2r - 2r r – 17 ≥ 14 + 17 + 17 {r|r ≥ 31} 3(31) - 17 = 2(31) + 14 • Draw “the river” • Subtract 2r from both sides • Simplify • Add 17 to both sides • Simplify in Set Notation • Check your limit • Graph the solution 10) Solve 3r - 17 ≥ 2r + 14

  12. Answer Now 11) Solve -2x + 6 ≥ 3x - 4 • {x|x ≥ -2} • {x|x ≤ -2} • {x|x ≥ 2} • {x|x ≤ 2}

  13. Answer Now 12) Joanna’s tests were 87, 93, 88 and 94. What must her 5th grade be to get a total of at least 459? • 96 • 97 • 98 • 100

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