Solve and graph the following absolute value inequalities. Express the solution in interval notation.
(A) $\mid 2x+0.6\mid >2.6$

• A. $(-1.6,1)$
• B. $x<-1.6$ OR $x>1$
• C. $x<-1$ OR $x>1.6$
• D. $\left(-1,1.6\right)$

Answer: (B)

Verified step by step guidance

1. 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 \(A < -B\).
2. 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$.
3. 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$.
4. 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$.
5. 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 \((-\infty, -1.6) \cup (1.0, \infty)\).