1 / 10

Algebra 1

Algebra 1. 6.5 Solving Absolute Value Equations and Inequalities. Steps to Solve an Absolute Value Equation. Isolate the absolute value expression Drop the absolute value and create a positive and a negative equation Solve each. Solving an Absolute Value Equation. Solve lx – 4l = 8

giulia
Télécharger la présentation

Algebra 1

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Algebra 1 6.5 Solving Absolute Value Equations and Inequalities

  2. Steps to Solve an Absolute Value Equation • Isolate the absolute value expression • Drop the absolute value and create a positive and a negative equation • Solve each

  3. Solving an Absolute Value Equation • Solve lx – 4l = 8 x – 4 = 8 or x – 4 = -8 +4 +4 +4 +4 x = 12 or x = -4 Mentally check your answers.

  4. Solving an Absolute Value Equation • Solve l5x + 1l + 3 = 14 Isolate the absolute value expression. l5x + 1l = 11 5x + 1 = 11 or 5x + 1 = -11 -1 -1 -1 -1 5x = 10 or 5x = -12 x = 2 or x = - 2 and 2/5 Mentally check your answers. -3 -3 5 5

  5. 1) lxl ≤ 2 (The distance from 0 is less than or equal to 2) 2) lxl > 3 (The distance from 0 is greater than 3) 3) lx + 2l ≥ 1 4) lx – 3l ≤ 2 Investigating Absolute-Value InequalitiesSee if each number is a solution as it appears. If it is, fill it in. . . . . . . . . . . . . . . . -5 -4 -3 -2 -1 0 1 2 3 4 5 -5 -4 -3 -2 -1 0 1 2 3 4 5 x ≤ 2 and x ≥ -2 or . . . . . . . . . . . . . -5 -4 -3 -2 -1 0 1 2 3 4 5 -4 -3 -2 -1 0 1 2 3 4 5 6 x > 3 or x < -3 WHY? and Absolute Value < or ≤ is an and inequality Absolute Value > or ≥ is an or inequality

  6. Steps to Solve an Absolute Value Inequality • Isolate the Absolute Value Expression • Drop the absolute value and create a positive inequality and a negative inequality (flip the sign) • Solve each inequality separately • <, ≤ is an and inequality >, ≥ is an or inequality 5) Graph

  7. Let’s Try! Solve lx + 6l < 8 x + 6 < 8 and x + 6 > -8 -6 -6 -6 -6 x < 2 and x > -14 0 2 -14

  8. You Try! Solve l2x - 4l ≥ 2 2x - 4 ≥ 2 or 2x - 4 ≤ -2 +4 +4 +4 +4 2x ≥ 6 or 2x ≤ 2 x ≥ 3 or x ≤ 1 1 2 3 0

  9. Let’s Try! Solve l2x + 1l - 3 ≥ 6 l2x + 1l – 3 ≥ 6 +3 +3 l2x + 1l ≥ 9 2x + 1 ≥ 9 or 2x + 1 ≤ -9 -1 -1 -1 -1 2x ≥ 8 or 2x ≤ -10 x ≥ 4 or x ≤ -5 -5 4 0

  10. You Try! Solve l3x - 3l + 4 < 10 l3x - 3l + 4 < 10 -4 -4 l3x - 3l < 6 3x - 3 < 6 and 3x - 3 > -6 +3 +3 +3 +3 3x < 9 and 3x > -3 x < 3 and x > -1 -1 3 0

More Related