Question 151534

{{{(5/4)x-1/8-1/3<2/3}}} Distribute.

{{{24((5/cross(4))x-1/cross(8)-1/cross(3))<24(2/cross(3))}}} Multiply both sides by the LCD {{{24}}} to clear any fractions.

{{{30x-3-8<16}}} Distribute and multiply.

{{{30x-11<16}}} Combine like terms on the left side.

{{{30x<16+11}}} Add {{{11}}} to both sides.

{{{30x<27}}} Combine like terms on the right side.

{{{x<(27)/(30)}}} Divide both sides by {{{30}}} to isolate {{{x}}}.

{{{x<9/10}}} Reduce.

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Which approximates to {{{x<0.9}}}

So the solution set is  *[Tex \LARGE \left\{x\|x<\frac{9}{10}\right\}]

Also, the answer in interval notation is *[Tex \LARGE \left(-\infty,\frac{9}{10}\right)]

Here's the graph of the solution set

{{{drawing(500,80,-5, 10,-10, 10,
number_line( 500, -5, 10),

arrow(9/10,0,-5,0),
arrow(9/10,0.30,-5,0.30),
arrow(9/10,0.15,-5,0.15),
arrow(9/10,-0.15,-5,-0.15),
arrow(9/10,-0.30,-5,-0.30),

circle(9/10,0,0.2),
circle(9/10,0,0.2),
circle(9/10,0,0.2),
circle(9/10,0,0.2-0.02)
)}}}

Note: there is an open circle at {{{x=0.9}}}