Download 2 Find Absolute Value 3 Solve an Absolute Value

2
EXAMPLE
Find Absolute Value
Evaluate the expression.
冨冨
1
c. 2
b. ⏐2.3⏐
a. ⏐5⏐
d. ⏐8⏐
Solution
a. ⏐5⏐ 5
If a is positive, then ⏐a⏐ a.
b. ⏐2.3⏐ (2.3)
If a is negative, then ⏐a⏐ a.
Use definition of opposites.
2.3
冢冣
冨冨
1
1
c. 2
2
1
2
1
2
1
2
The absolute value of is .
Use definition of opposites.
d. ⏐8⏐ (8)
The absolute value of 8 is 8.
Use definition of opposites.
8
Find Absolute Value
Evaluate the expression.
1. ⏐4⏐
Student Help
LOOK BACK
For help with the
solution of an
equation, see p. 24.
EXAMPLE
冨冨
3
3. 2
2. ⏐0⏐
3
4. ⏐1.7⏐
Solve an Absolute Value Equation
Use mental math to solve the equation.
a. ⏐x⏐ 7
b. ⏐x⏐ 5.1
2
c. ⏐x⏐ 9
Solution
a. Ask, “What numbers are 7 units from 0?” Both 7 and 7 are 7 units from
0, so there are two solutions: 7 and 7.
b. Ask, “What numbers are 5.1 units from 0?” Both 5.1 and 5.1 are 5.1
units from 0, so there are two solutions: 5.1 and 5.1.
c. The absolute value of a number is never negative, so there is no solution.
Solve an Absolute Value Equation
Use mental math to solve the equation. If there is no solution, write
no solution.
5. ⏐x⏐ 4
72
Chapter 2
Properties of Real Numbers
6. ⏐x⏐ 1.5
1
7. ⏐x⏐ 6