1. Solving Equations with Absolute Values
August 25th, 2016

2. Absolute Value
The absolute value of a number is its distance from 0 on the number line. Since distance is nonnegative, the absolute value of a number is always nonnegative.
The symbol 𝑥 is used to represent the absolute value of a number x.
Example: −3 =3 and 3 =3
3 units
3 units

3. Evaluating an Expression with an Absolute Value
Example: Evaluate 𝑦 −7 if 𝑦=− 𝑦−7 = −3 −7 Replace y with -3 =1.4+ −15 −7 Simplify 5(-3) first. =1.4+ −22 Subtract 7 from -15 = −22 =22 =23.4 Add.

4. Absolute Value Equations
Some equations contain absolute value expressions.
The definition of absolute value is used in solving these equations.
Note
𝑥 =5
𝑥=5 𝑜𝑟 −5

5. Solve an Absolute Value Equation
Solve 𝑥−18 =5. Check your solutions Note: There are two parts to every absolute value equation, so we will look at each part individually.

6. Solve 𝑥−18 =5 Case 1
𝑥−18=5 𝑥−18+18=5+18 𝑥=23 Check: 𝑥−18 =5 23−18 =5 5 =5 5=5

7. Solve 𝑥−18 =5 Case 2
𝑥−18=−5 𝑥−18+18=−5+18 𝑥=13 Check: 𝑥−18 =5 13−18 =5 −5 =5 5=5

8. You try! (REMEMBER TO CHECK YOUR ANSWERS!)
𝑥−25 =17
2 𝑏+4 =48
𝑥={8, 42}
𝑏={−28, 20}