Solve the inequality 5≤3+|2x−7|

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Prince Huang · Accepted Answer

5≤3+|2x−7|    Simplify the expression    3+|2x−7|≥5    3+|2x−7|−3≥5−3 (subtract 3 from both sides)    |2x−7|≥2    By the absolute rule, if |u|≥a,a&amp;gt;0 then |u|≤−a and |u|≥a    2x−7≤−2 and 2x−7≥2 (by the absolute rule)    2x−7+7≤−2+7 and 2x−7+7≥2+7 (add 7 on both sides)    2x≤5 and 2x≥9    2x2≤52 and 2x2≥92 (divide by 2)    x≤52 and x≥92    Thus, the solution is (−∞,52]∪[92,∞)

Solve the inequality 5≤3+|2x−7|

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