What is 3((x+1))/2-x-1/4 < 1/2 ?

The solution to 3((x+1))/2-x-1/4 < 1/2 is x<-3/2

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3((x+1))/2-x-1/4 < 1/2

3 \frac{( x + 1 )}{2} - x - \frac{1}{4} < \frac{1}{2}

x < - \frac{3}{2}

Interval Notation

(- \infty, - \frac{3}{2})

Decimal Notation

x < - 1.5

Solution steps

3 \cdot \frac{( x + 1 )}{2} - x - \frac{1}{4} < \frac{1}{2}

Multiply

3 \cdot \frac{x + 1}{2} : \frac{3 ( x + 1 )}{2}

\frac{3 ( x + 1 )}{2} - x - \frac{1}{4} < \frac{1}{2}

Move

\frac{1}{4}

to the right side

\frac{3 ( x + 1 )}{2} - x < \frac{3}{4}

Multiply both sides by

2

3 (x + 1) - 2 x < \frac{3}{2}

Expand

3 (x + 1) - 2 x : x + 3

x + 3 < \frac{3}{2}

Move

3

to the right side

x < - \frac{3}{2}

\frac{( 4 x + 2 )}{3} \leq \frac{( 25 - 2 x )}{4}

4 (x + 7) > 3 (x + 2)

5 - 2 x \leq 3

∣ 2 ∣ \cdot x ∣ - 3 ∣ < 1

\frac{x - 4}{5} > \frac{1}{5}

What is 3((x+1))/2-x-1/4 < 1/2 ?
The solution to 3((x+1))/2-x-1/4 < 1/2 is x<-3/2