How do you solve #\frac { - x + 2} { 2} - \frac { 1- 7x } { 8} < - 10#?

1 Answer
Jim G.
Dec 28, 2016

#x< -29#

Explanation:

If we multiply ALL terms on both sides of the inequality by the lowest common multiple ( LCM) of 2 and 8, which is 8 then we 'eliminate' the fractions.

#(cancel(8)^4xx(-x+2)/cancel(2)^1)-(cancel(8)^1xx(1-7x)/cancel(8)^1)<(8xx-10)#

#rArr4(-x+2)-1(1-7x)<-80#

distributing the brackets.

#-4x+8-1+7x<-80#

simplifying left side by collecting like terms.

#rArr3x+7<-80#

subtracting 7 from both sides.

#3xcancel(+7)cancel(-7)<-80-7#

#rArr3x<-87#

To solve for x, divide both sides by 3

#(cancel(3) x)/cancel(3)<(-87)/3#

#rArrx<-29" is the solution"#

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