Solving Absolute Value Equations and Inequalities By Ellie Silverman

Solving Absolute Value Equations 2x + 3 = 7

2x + 3 = 7 This equation means the absolute value of 2x+3 is 7. These are absolute value signs This equation means the absolute value of 2x+3 is 7. Absolute value is a number’s 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. 1 2 3 4 1 2 3 4 -4 -3 -2 -1 1 2 3 4

2x + 3 = 7 To 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 = 7 2x + 3 = -7

Now that you set 2x+3 equal to 7 and -7, you solve. -3 -3 -3 -3 2x = 4 2x = -10 2 2 2 2 x = -5 x = 2

Solving Absolute Value Inequalities 2x + 3 < 7 2x + 3 > 7 2x + 3 ≤ 7 2x + 3 ≥ 7

Some things to remember when solving inequalities: * 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 > = open dot on number line * ≤ or ≥ = closed dot on number line

2x + 3 < 7 2x + 3 < 7 2x + 3 > -7 and Less thand 2x + 3 < 7 To 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 -7 2x + 3 < 7 2x + 3 > -7 and

Now that you set 2x+3 less than 7 and -7, you solve. -3 -3 -3 -3 2x < 4 2x > -10 2 2 2 2 x < 2 x > -5

X < 2 AND X > -5 X ≤ 2 AND X ≥ -5 Now it’s time to graph your solutions! X < 2 AND X > -5 -6 -5 -4 -3 -2 -1 1 2 3 4 5 If the answer looked like this: X ≤ 2 AND X ≥ -5 Then the circles on the graph would be closed

2x + 3 > 7 2x + 3 > 7 2x + 3 < -7 or greator 2x + 3 > 7 To 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 -7 2x + 3 > 7 2x + 3 < -7 or

Now that you set 2x+3 greater than 7 and less than -7, you solve. -3 -3 -3 -3 2x > 4 2x < -10 2 2 2 2 x > 2 x < -5

X > 2 OR x < -5 X ≥ 2 OR x ≤ -5 Now it’s time to graph your solutions! X > 2 OR x < -5 -6 -5 -4 -3 -2 -1 1 2 3 4 5 If the answer looked like this: X ≥ 2 OR x ≤ -5 Then the circles on the graph would be closed

Solve and graph each inequality: More Practice Solve and graph each inequality: 1.) 8b + 9 < 63 5.) -7r ≤ 7 6.) 8b + 9 < 63 2.) 4 + 5x > 24 3.) 5 - 8x < 43 7.) -5p ≥ 20 4.) -8x - 10 < 58 3.) 1 + x < 8

Just a Funny Math Video http://www.youtube.com/watch?v=6cAs1YBELmA