[br]In a previous lesson, you learned about the concept of absolute value.[br][br][i][color=#0000ff]Going the Distance:[/color][/i] https://www.geogebra.org/m/fyuu6q6n[br][br]In this lesson, you'll learn how to solve absolute value equations.

[br]Step 1: Isolate the [color=#0000ff]absolute value[/color] expression.[br][br]Step 2: Check the [color=#0000ff]number[/color] on the other side of the equation. [br][br] There are [color=#0000ff]three[/color] cases:[br][br] Case 1: If the number is negative ( − ), there is [color=#ff0000]no solution[/color].[br][br] Case 2: If the number is zero ( 0 ), there is [color=#ff0000]one solution[/color]. Remove the absolute value symbol from the [color=#0000ff]absolute value[/color] expression, and solve for the unknown.[br][br] Case 3: If the number is positive, there are [color=#ff0000]two solutions.[/color] Equate the algebraic expression inside the absolute value symbol to both the positive ( + ) and the negative ( − ) value of the number on the other side, and solve for the unknowns.[br][br]Step 3: Verify your answer/s.[br][br]Examples:[br][br]|2x − 4| = −10 ➽ [color=#6aa84f]No solution.[/color][br] [br]|2x − 4| = 0 ➽ 2x − 4 = 0 [br][br] 2x = 4[br][br] x = [color=#6aa84f]2[/color][br][br]|2x − 4| = 10 ➽ 2x − 4 = 10 or 2x − 4 = −10 [br][br] 2x = 14 2x = −6[br][br] x = [color=#6aa84f]7 [/color]x =[color=#6aa84f] −3[/color]

[br]Solve the problems first on a separate sheet of paper and then type your answers in the boxes provided. Click the question mark to check your answers. If your answers are correct, a big [color=#ff00ff]"Correct!!!"[/color] sign will appear. Otherwise, you'll have to redo the problem.[br][br]Repeat as many times as needed to master the concept.

In future lessons, you'll also learn how to solve absolute value inequalities. Did you ENJOY today's lesson?