Page 503 - Algebra 1

Example
1
Solving Absolute-Value Equations
Solve.
a. ⎢x =7
SOLUTION Using the definition of absolute value, x is a number that is 7 units from 0. So, ⎢x⎥ = 7 means that x = 7 or that x = -7.
Caution
When rewriting the absolute-value equation as two equations, do not use the absolute-value symbols.
The solution is {7, -7}. Check
⎪x⎥ = 7 ⎪7⎥ 7
7=7 ✓
⎢x⎥ = 7 ⎪-7⎥ 7
7=7 ✓
b. ⎢x+3 =16
SOLUTION Write ⎪x + 3 = 16 as two equations.
x + 3 = 16 or
x = 13 Subtract 3 from both sides.
x + 3 = -16 x = -19
16=16 ✓
In some equations it is necessary to first isolate the absolute-value term.
Math Reasoning
Write Use the definition of absolute value to give the meaning of
⎢x + 3 = 16.
The solution is {13, -19}. Check
⎪x + 3 = 16 ⎪13 + 3 16 ⎪16 16
⎪x + 3 = 16 ⎪-19 + 3 16 ⎪-16 16
Isolating the Absolute Value
5⎢x = 20 __
55 ⎢x = 4.
The equation ⎢x = 4 means that x = 4 or that x = -4. The solution set is {4, -4}.
16=16 ✓
Example
2
Solve.
a. 5⎢x = 20 SOLUTION
488 Saxon Algebra 1
Check
5⎪x = 20 5⎪4 20 5 · 4 20
5⎪x = 20 5⎪-4 20 5 · 4 20
20=20 ✓
20=20 ✓