Question

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

Answer 1

Answer:

$x\le \:-1$

Step-by-step explanation:

$3\left(x-1\right)\le \frac{1}{2}\left(x+1\right)-6$

$3x-3\le \:-\frac{11}{2}+\frac{1}{2}x$

$3x\le \:-\frac{5}{2}+\frac{1}{2}x$

$\frac{5}{2}x\le \:-\frac{5}{2}$

$5x\le \:-5$

$x\le \:-1$

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 ≤ $-\frac{13}{2}$

This is also true.

Therefore, x ≤ -1.