solving absolute value equations

Solving Absolute Value Equations : 

Solving Absolute Value Equations Mrs. Thomas

Absolute Value (of x) : 

Absolute Value (of x) Symbol lxl The distance x is from 0 on the number line. Always positive Ex: l-3l= 3 -4 -3 -2 -1 0 1 2

Ex: x = 5 : 

Ex: x = 5 What are the possible values of x? x = 5 or x = -5

Slide 4: 

You can solve some absolute-value equations using mental math. For instance, you learned that the equation | x | 8 has two solutions: 8 and 8. To solve absolute-value equations, you can use the fact that the expression inside the absolute value symbols can be either positive or negative.

Steps to Solving Absolute Value Equations : 

Steps to Solving Absolute Value Equations Step One: Isolate the absolute value expression. Step Two: Set up two equations to solve. For the first equation, drop the absolute value bars and solve the equation. For the second equation, drop the bars, negate the opposite side, and solve the equation. Step Three: Always check the solutions.

How Should the Steps of the Process Look? : 

How Should the Steps of the Process Look? ax+b = c, where c>0 To solve, set up 2 new equations, then solve each equation. ax+b = c or ax+b = -c ** Make sure the absolute value is by itself before you split to solve.

Solve: 6x-3 = 15 : 

Solve: 6x-3 = 15 6x-3 = 15 or 6x-3 = -15 6x = 18 or 6x = -12 x = 3 or x = -2 * Plug in answers to check your solutions!

Slide 8: 

Solve | x  2 |  5 x  2 IS POSITIVE | x  2 |  5 x  7 x  3 x  2 IS NEGATIVE | x  2 |  5 | 7  2 |  | 5 |  5 | 3  2 |  | 5 |  5 The expression x  2 can be equal to 5 or 5. x  2  5 Solve | x  2 |  5 SOLUTION x  2  5 The equation has two solutions: 7 and –3.

Slide 9: 

Solve | 2x  7 |  5  4 2x  7 IS POSITIVE | 2x  7 |  5  4 | 2x  7 |  9 2x  7  +9 2x  16 2x  7 IS NEGATIVE | 2x  7 |  5  4 | 2x  7 |  9 2x  7  9 2x  2 x  1 Isolate the absolute value expression on one side of the equation. SOLUTION Solve | 2x  7 |  5  4 x  8

Solve 2x + 7 - 3 = 8 : 

Solve 2x + 7 - 3 = 8 Isolate the absolute value part first! 2x+7 = 11 Now split into 2 parts. 2x+7 = 11 or 2x+7 = -11 2x = 4 or 2x = -18 x = 2 or x = -9 Check the solutions.

Solve 4x + 7 = -3 : 

Solve 4x + 7 = -3 Solution This equation has NO SOLUTION, since the answer to an absolute value equation cannot be negative. Absolute value is a distance and distances cannot be negative.

Solve 4x + 6 + 8= 3 : 

Solve 4x + 6 + 8= 3 4x + 6 + 8= 3 -8 -8 4x + 6 = -5 No solution! But why?