College Algebra 9th txtbk

70 CHAPTER 1 EQUATIONS AND INEQUALITIES
SOLUTIONS (A) 3x 5 4 Use Theorem 3, part 1 (B) x 6 5 Use Theorem 2, part 2
3x 5 4
5 6 x 6 5
3x 5 4
or (5, 5)
x 5 4
3
x 3, 1 3
or 53, 1 36
(C) 2x 1 6 3 Use Theorem 3, part 2 (D) 7 3x 2 Use Theorem 3, part 2
3 6 2x 1 6 3
2 7 3x 2
2 6 2x 6 4
9 3x 5
1 6 x 6 2
3 x 5 3
5
or (1, 2)
3 x 3
or [ 5 3, 3]
MATCHED PROBLEM 4
Solve each equation or inequality. For inequalities, write solutions in both inequality and
interval notation.
(A) 2x 1 8 (B) x 7 (C) 3x 3 9 (D) 5 2x 6 9
EXAMPLE 5 Solving Absolute Value Inequalities
Solve, and write solutions in both inequality and interval notation.
(A) x 7 3 (B) 2x 1 3 (C) 7 3x 7 2
SOLUTIONS (A) x 7 3
x 6 3 or x 7 3
(, 3) (3, )
Use Theorem 2, part 3.
Solution in inequality notation
Solution in interval notation
(B) 2x 1 3
2x 1 3 or 2x 1 3
Use Theorem 3, part 3.
Add 1 to both sides.
2x 2 or
x 1 or
(, 1] [2, )
2x 4
x 2
Divide both sides by 2.
Solution in inequality notation
Solution in interval notation
(C) 7 3x 7 2
Use Theorem 3, part 3.
7 3x 6 2 or 7 3x 7 2 Subtract 7 from both sides.
3x 6 9 or 3x 7 5 Divide both sides by 3 and reverse the direction of
the inequality.
x 7 3 or x 6 5 3
(, 5 3) (3, )
Solution in inequality notation
Solution in interval notation
MATCHED PROBLEM 5
Solve, and write solutions in both inequality and interval notation.
(A) x 5 (B) 4x 3 7 5 (C) 6 5x 7 16