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Solve the compound inequality 12x − 4 < 3 and 7 ≤ 3x + 5.

User RichardLiu
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1 Answer

6 votes


12x-4 < 3

Add 4 to both sides:


12x-4+4 < 3+4


12x < 7

Divide both sides by 12:


(12x)/(12) < (7)/(12)


\fbox{x} < \fbox{$(7)/(12) $}

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7\leq 3x+5

Flip:


3x+5\geq 7

Subtract 5 from both sides:


3x+5-5\geq 7-5


3x\geq 2

Divide both sides by 3:


(3x)/(3) \geq (2)/(3)


\fbox{x}\geq \fbox{$(2)/(3) $}

User Gergely Orosz
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3.1k points