1. 2.5 Solving Equations Involving Absolute Value
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2. CC Standards Explain each step in solving simple equation.
Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

3. 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

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

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

6. 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.

7. 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
|x + 4| = -4 no solution

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

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