In many cases, it can be helpful to view the solutions to absolute value equations and inequalities as follows. For any algebraic expression X and positive constant k, the equation |X| = k has solutions X = kand −X = k, since the absolute value of either quantity on the left will indeed yield the positive constant k. Likewise, |X| < k has solutions X < kand −X < k. Note the inequality symbol has not been reversed as yet, but will naturally be reversed as part of the solution process. Solve the following equations or inequalities using this idea.
a. |x − 3| = 5
b. |x − 7| > 4
c. 3|x + 2| ≤ 12
d. −3|x − 4| + 7 = −11
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