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

2 Answers
ali ergin
Mar 19, 2017

{x<=-3" or "x>=1/7}{x≤−3 or x≥17}

Explanation:

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

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

-10-7x>=11−10−7x≥11

-7x>=11+10−7x≥11+10

-7x>=21−7x≥21

-x>=21/7−x≥217

-x>=3−x≥3

x<=-7x≤−7

"if positive : "if positive :

10+7x>=1110+7x≥11

7x>=11-107x≥11−10

7x>=17x≥1

x>=1/7x≥17

Jim G.
Mar 19, 2017

x>=1/7" or " x<=-3x≥17 or x≤−3

Explanation:

This inequality is of the form.

|x|>=arArrxcolor(red)(>=)a" or " xcolor(red)(<=)-a|x|≥a⇒x≥a or x≤−a

There are 2 possible solutions here.

10+7xcolor(red)(>=)11" or " 10+7xcolor(red)(<=)-1110+7x≥11 or 10+7x≤−11

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

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