How do you solve the inequality: #-1/6<= 4x-4<1/3#?

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Answer 1 · 2015-08-31T00:29:29

#x in [23/24, 26/24)#

You need to isolate #x# between the two inequality signs. Start by adding #4# to all sides

#-1/6 + 4 <= 4x - color(red)(cancel(color(black)(4))) + color(red)(cancel(color(black)(4))) < 1/3 + 4#

#23/6 <= 4x < 13/3#

Now divide all sides by #4#

#23/6 * 1/4 <= (color(red)(cancel(color(black)(4)))x)/color(red)(cancel(color(black)(4))) < 13/3 * 1/4#

This will get you

#23/24 <= x < 13/12#

which is equivalent to

#23/24 <= x < 26/24#

In interval notation, the solution set for this compound inequality is #x in [23/24, 26/24)#.