Solve the compound inequality 1/2 x − 4 < 3 and 7 ≤ 3x + 5.

Question

asked Sep 18, 2023 119k views

1 Answer

Pavel Krymets · Answer 1 · 2023-09-25T01:57:50+0000

$(1)/(2) x - 4 < 3 \\$

Add both sides 4

$(1)/(2) x - 4 + 4 < 3 + 4 \\$

$(1)/(2) x < 7 \\$

Multiply both sides by 2

$2 * (1)/(2) x < 2 * 7 \\$

x < 14

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$7 \leqslant 3x + 5$

$3x + 5 \geqslant 7$

Subtract both sides minus 5

$3x + 5 - 5 \geqslant 7 - 5$

$3x \geqslant 2$

Divide both sides by 3

$(3x)/(3) \geqslant (2)/(3) \\$

$x \geqslant (2)/(3) \\$