Multiple Choice
Solve and graph the following absolute value inequalities. Express the solution in interval notation.
(A)
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2. Linear Equations and Inequalities
Absolute Value Inequalities
Multiple Choice
Solve and graph the following absolute value inequalities. Express the solution in interval notation.
(A)
A
B
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C
OR
D
Verified step by step guidance1
Recall that for an absolute value inequality of the form \(\left|A\right| > B\), where \(B > 0\), the solution splits into two cases: \(A > B\) or \(A < -B\).
Apply this rule to the inequality \(\left|2x + 0.6\right| > 2.6\), which gives two inequalities to solve: \$2x + 0.6 > 2.6\( and \)2x + 0.6 < -2.6$.
Solve the first inequality \$2x + 0.6 > 2.6\( by isolating \)x\(: subtract \)0.6\( from both sides to get \)2x > 2.0\(, then divide both sides by \)2\( to find \)x > 1.0$.
Solve the second inequality \$2x + 0.6 < -2.6\( by subtracting \)0.6\( from both sides to get \)2x < -3.2\(, then divide both sides by \)2\( to find \)x < -1.6$.
Express the solution as the union of the two intervals found: \(x < -1.6\) or \(x > 1.0\), and write this in interval notation as \((-\infty, -1.6) \cup (1.0, \infty)\).
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