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

Question

asked Jul 15, 2023 183k views

1 Answer

Gergely Orosz · Answer 1 · 2023-07-20T16:14:15+0000

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) $}$