9.3 equations and absolute value goal(s): to solve equations involving absolute value
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9.3 Equations and Absolute Value
Goal(s): To solve equations involving absolute value
Solve: |x - 3| = 2
• What values can be substituted for “x” to make the equation true?
5 or x 1
Solving Equations with Absolute ValuesTo solve an equation of the form
|A| = bSolve the disjunctionA = b or A = -b
Solve for “x”: |x + 3| = 7
x + 3 = 7
x + 3 = -7
Do not write the absolute value brackets when you set up the two different
equations.
Solve |2x – 4| = 10
x = 7
2 4 10x 2 14x
2 4 10x
2 6x 4 4
3x or
Solve |2x + 5| = 13
x = 4 or x = -9
Solve |3x + 7| = 19
264 or 3
x x
Solve |5x – 3| = -17
No solution. The solution set is
Solving |absolute value| equations:
The absolute value expression must be “by itself” before writing the two different equations.
113 7 |2x+5|7 7
3 | 2 5 | 18x 3 3
| 2 5 | 6x
Solve: |2x – 7| + 5 = 12
| 2 7 | 7x
2 7 7x 2 14x
7x
2 7 7x 2 0x
0x or
Solve |2x + 5| -9 = 12
x = 8 or x = -13
+9 +9|2x + 5| = 21
Solve: 3|2x + 5| -9 = 12
x = 1 or x = -6
+9 +93|2x + 5| = 213 3
2x + 5 = 7 2x + 5 = -7
Assignment:Page 412
(12-32) even
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