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You can use a number line to write an absolute-value equation that has two given
numbers as its solutions.
Write an Absolute-Value Equation
4
EXAMPLE
Write an absolute-value equation that has 7 and 15 as its solutions.
Solution
Graph the numbers on a number line and locate the midpoint of the graphs.
4 units
6
7
8
4 units
9
10
11
12
13
14
15
16
The graph of each solution is 4 units from the midpoint, 11. You can use the
midpoint and the distance to write an absolute-value equation.
Midpoint
Distance
⏐x 11⏐ 4
ANSWER 䊳 The equation is ⏐x 11⏐ 4. Check that 7 and 15 are solutions
of this equation.
5
EXAMPLE
Animals
Write an Absolute-Value Equation
The shoulder height of the shortest miniature poodle is 10 inches.
The shoulder height of the tallest is 15 inches. Write an absolute-value equation
that has these two heights as its solutions.
POODLES
Solution
Graph the numbers on a number line and locate the midpoint of the graphs.
Then use the method of Example 4 to write the equation.
2.5 units
2.5 units
Shoulder height
9
POODLES A poodle is
labeled a toy, a miniature, or
a standard based on its
shoulder height. The smallest
poodle is the toy. The largest
is the standard.
10
11
12 12.5 13
14
15
16
The midpoint is 12.5. Each solution is 2.5 units from 12.5.
Midpoint
Distance
⏐x 12.5⏐ 2.5
ANSWER 䊳 The equation is ⏐x 12.5⏐ 2.5. Check that 10 and 15 are
solutions of this equation.
Write an Absolute-Value Equation
10. Write an absolute-value equation that has 4 and 12 as its solutions.
6.6
Solving Absolute-Value Equations
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