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

2 Answers
Mar 19, 2017

Answer:

#{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#

Mar 19, 2017

Answer:

#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"#