How do you solve the inequality #-a/7+1/7>1/14#?

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Answer 1 · 2017-01-19T10:13:41

#color(green)(a<1/2)#

A fraction consists of #("count")/("size indicator") ->("numerator")/("denominator")#

You can not directly compare the counts (numerators) unless the size indicators (denominators) as the same.

#color(green)([-a/7color(red)(xx1)]+[1/7color(red)(xx1)] >1/14)#

#color(green)([-a/7color(red)(xx2/2)]+[1/7color(red)(xx2/2)] >1/14)#

#color(green)(" "-(2a)/14" "+" "2/14" ">1/14#

Now that the denominators are all the same the inequality is still true if we compare only the counts (numerators).

#" "color(green)(-2a+2>1)#

Divide both sides by 2

#" "color(green)(-a+1>1/2)#

Subtract 1 from both sides

#" "color(green)(-a>1/2-1)#

#" "color(green)(-a > -1/2)#

Multiply both sides by (-1) and turn the inequality round the other way. You always turn the inequality if multiply by any negative value.

#" "color(green)(a<1/2)#