2.5 Solving Equations Involving Absolute Value 9/28/16

CC Standards Explain each step in solving simple equation. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

Absolute Value In Expressions (without =) |5| = 5 ONLY 1 ANSWER |-3| = 3 |4 – 9| = 5 In Equations (with an =) |n + 7| = 5 In an equation, you will always have 2 outcomes. |n + 7| = 5 or |n + 7| = -5 Then solve for 2 equations. |x| = 9 x = 9 or x = - 9

Absolute Value Expressions (without an =) Expressions involving absolute value can be evaluated using the given value for the variable. Evaluate |3 – h| + 13 if h = 5 Substitute 5 for variable h |3 – 5| + 13 |-2| + 13 The absolute value of -2 is 2 2 + 13 = 15

Absolute Value Expressions |4 + x| + 7 if x = - 9 Substitute for x. |4 + (-9)| + 7 Add or sub? |-5| + 7 5 + 7 12 |x + 9| - 11 if x = 4 |4 + 9| - 11 |13| - 11 13 + (-11) 2

Absolute Value Equation then graph the solution set. |3z – 3| = 9 Remember, 2 outcomes with equations |3z – 3| = 9 or |3z – 3| = - 9 Solve both Graph its solution set.

Absolute Value Equations a b c a is the variable b is the other number in the absolute value c is the number outside of the absolute value If C value is a negative number or when you add or subtract the C value, the outcome will be a no solution. |3n – 4| = - 1 is no solution |x + 4| + 6 = 2 Isolate the absolute value before separating into 2 outcomes |x + 4| +6 = 2 -6 -6 |x + 4| = -4 no solution

Challenging Absolute Problems c= 2, z= - 4.2, a = - 2 -4|c – 3| + 2|z – a| 4 – 3|q| = 10

TOTD 10\12 Solve the absolute value equation |4d + 2| = 12