# Solving Absolute Value Equations and Inequalities

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Solving Absolute Value Equations and Inequalities. By Ellie Silverman. Solving Absolute Value Equations. 2 x + 3 = 7. 2 x + 3 = 7. These are absolute value signs. This equation means the absolute value of 2x+3 is 7. - PowerPoint PPT Presentation

### Text of Solving Absolute Value Equations and Inequalities

• Solving Absolute Value Equations and InequalitiesBy Ellie Silverman

• Solving Absolute Value Equations2x + 3 = 7

• 2x + 3 = 7This equation means the absolute value of 2x+3 is 7.Absolute value is a numbers distance from zero. For example, the absolute value of 4 is 4 and the absolute value of -4 is 4 because they are both four spots away from zero.These are absolute value signs4-20-1123-4-312341234

• 2x + 3 = 7To solve this equation you have to get rid of the absolute value signs. To do this you have to set 2x+3 equal to 7 and -7. 2x + 3 = 72x + 3 = -7

• 2x + 3 = 7 Now that you set 2x+3 equal to 7 and -7, you solve.2x + 3 = -7 2x = 42x = -102222x = 2x = -5-3 -3-3 -3

• Solving Absolute Value Inequalities2x + 3 < 72x + 3 72x + 3 > 72x + 3 7

• Some things to remember when solving inequalities:* < or > = open dot on number line

* Always remember to flip the sign if you divide by a negative* Less than means you put and between your solutions and shade between them on the number line* Greater means you put or between your solutions and shade outwards on the number line* or = closed dot on number line

• 2x + 3 < 7To solve this inequality you have to get rid of the absolute value signs. To do this you have to set 2x+3 less than 7 and greater than -7Less thand2x + 3 < 72x + 3 > -7and

• Now that you set 2x+3 less than 7 and -7, you solve.2x + 3 < 7and2x + 3 > -7-3 -3-3 -32x < 42x > -10x < 2x > -52222

• 4-20-1123-4-3Now its time to graph your solutions!5-5-6X < 2 AND X > -5

If the answer looked like this:X 2 AND X -5 Then the circles on the graph would be closed

• 2x + 3 > 7To solve this inequality you have to get rid of the absolute value signs. To do this you have to set 2x+3 greater than 7 and less than -7greator2x + 3 > 72x + 3 < -7or

• Now that you set 2x+3 greater than 7 and less than -7, you solve.2x + 3 > 7and2x + 3 < -7-3 -3-3 -32x > 42x < -10x > 2x < -52222

• 4-20-1123-4-3Now its time to graph your solutions!X > 2 OR x < -5

5-5-6If the answer looked like this:Then the circles on the graph would be closedX 2 OR x -5

• More PracticeSolve and graph each inequality:1.) 8b + 9 < 634.) -8x - 10 < 582.) 4 + 5x > 243.) 5 - 8x < 435.) -7r 7 6.) 8b + 9 < 637.) -5p 203.) 1 + x < 8

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