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Inequality Graphing and Solving Practice

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Learn to graph and solve inequalities with helpful tips and examples. Practice drawing river diagrams, switching inequalities, and checking solutions to master the concept.

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Inequality Graphing and Solving Practice

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  1. ObjectiveThe student will be able to: • graph inequalities on a number line. • solve inequalities using addition and subtraction. Designed by Skip Tyler, Varina High 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 • Check your answer • Graph the solution x- 14< 16 + 14 + 14 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 • Check your answer • Graph the solution - 21 -21 y ≥ -14 (-14) + 21 = 7 7 = 7

  9. ObjectiveThe student will be able to: solve inequalities using multiplication and division. Designed by Skip Tyler, Varina High School

  10. o -5 -4 -3 o -5 -4 -3 ● -5 -4 -3 -5 -4 -3 Answer Now 1) Which graph represents the correct answer to > 1 ●

  11. o -53 -52 -51 1) Solve > 13 • Draw “the river” • Clear the fraction - Multiply both sides by -4 • NEW STEP!! When multiplying BOTH sides by a NEGATIVE number, SWITCH the inequality! • Simplify • Check your answer • Graph the solution k < -52

  12. Answer Now 2) When solving > -10will the inequality switch? • Yes! • No! • I still don’t know!

  13. o -31 -30 -29 • Draw “the river” • Clear the fraction - Multiply both sides by 3. Do you switch the inequality? • No - Both sides are being multiplied by a positive number • Simplify • Check your answer • Graph the solution 2) Solve < -10 x < -30

  14. Answer Now 3) When solving will the inequality switch? • Yes! • No! • I still don’t know!

  15. o -25 -24 -23 3) Solve • Draw “the river” • Clear the fraction - Multiply both sides by -4. Do you switch the inequality? • Yes - Both sides are being multiplied by a negative number • Simplify • Check your answer • Graph the solution a > -24

  16. Take a quick break! Things that make you go.....Hmmm Why is abbreviation such a long word? Why do they have braille dots on the ATM machines in drive-thru’s?

  17. Answer Now 4) Solve -8p ≥ -96 • p ≥ 12 • p ≥ -12 • p ≤ 12 • p ≤ -12

  18. ● 11 12 13 4) Solve -8p ≥ -96 • Draw “the river” • Divide both sides by -8. Do you switch the inequality? • Yes - Both sides are being divided by a negative number • Simplify • Check your answer • Graph the solution p ≤ 12 -8(12) = -96

  19. o -16 -15 -14 o -16 -15 -14 ● -16 -15 -14 -15 -15 -14 Answer Now 5) Solve 7v < -105 ●

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