SOLUTION: 5/4[x-1/2]-5/3<4/3 Please help I need to use set builder to fill this in {x/x? ?}

Question 200028: 5/4[x-1/2]-5/3<4/3
Please help I need to use set builder to fill this in
{x/x? ?}
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given inequality.

Add to both sides.

Combine like terms.

Reduce

Multiply both sides by 4.

Multiply

Divide both sides by 5.

Break up the absolute value (remember, if you have , then and )

and Break up the absolute value inequality using the given rule

Combine the two inequalities to get a compound inequality

Multiply EVERY term on ALL sides by the LCD 10 to clear out the fractions.

Multiply and simplify

Add to ALL sides.

Combine like terms on the left side.

Combine like terms on the right side.

Divide all sides by 10.

So the solution is

So the answer in set-builder notation is

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