Question

How do you solve `abs(10+7x)>=11`?

Answer 1

`{x<=-3" or "x>=1/7}`

Explanation:

`"The expression of |10+7x| may be positive or negative"`

`"if negative : " -(10+7x)>=11`

`-10-7x>=11`

`-7x>=11+10`

`-7x>=21`

`-x>=21/7`

`-x>=3`

`x<=-7`

`"if positive : "`

`10+7x>=11`

`7x>=11-10`

`7x>=1`

`x>=1/7`

Answer 2

`x>=1/7" or " x<=-3`

Explanation:

This inequality is of the form.

`|x|>=arArrxcolor(red)(>=)a" or " xcolor(red)(<=)-a`

There are 2 possible solutions here.

`10+7xcolor(red)(>=)11" or " 10+7xcolor(red)(<=)-11`

`color(blue)"Solving " 10+7x>=11`

subtract 10 from both sides.

`cancel(10)cancel(-10)+7x>=11-10`

`rArr7x>=1`

divide both sides by 7

`(cancel(7) x)/cancel(7)>=1/7`

`rArrx>=1/7larrcolor(red)" first solution"`

`color(blue)"Solving " 10+7x<=-11`

`rArr7x<=-21`

`rArrx<=-3larrcolor(red)" second solution"`