3(x-1)≤ ½(x+1) -6. Topic is Linear inequalities

Question

asked Apr 15, 2022 208k views

1 Answer

Diego Alvis · Answer 1 · 2022-04-20T21:59:15+0000

Answer:

$x\le \:-1$

Explanation:

$3\left(x-1\right)\le (1)/(2)\left(x+1\right)-6$

$3x-3\le \:-(11)/(2)+(1)/(2)x$

$3x\le \:-(5)/(2)+(1)/(2)x\\$

$(5)/(2)x\le \:-(5)/(2)$

$5x\le \:-5$

$x\le \:-1$

x = -1

3(-2) ≤ ½(0) - 6

-6 ≤ 0 - 6

-6 ≤ -6

This is true.

x = -2

3(-3) ≤ ½(-1) - 6

-9 ≤ -½ - 6

-9 ≤
-(13)/(2)

This is also true.

Therefore, x ≤ -1.