What is ((1-2x))/3+((x-2))/6 >((x+3))/2-1 ?

The solution to ((1-2x))/3+((x-2))/6 >((x+3))/2-1 is x<-1/2

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((1-2x))/3+((x-2))/6 >((x+3))/2-1

\frac{( 1 - 2 x )}{3} + \frac{( x - 2 )}{6} > \frac{( x + 3 )}{2} - 1

x < - \frac{1}{2}

Interval Notation

(- \infty, - \frac{1}{2})

Decimal Notation

x < - 0.5

Solution steps

\frac{( 1 - 2 x )}{3} + \frac{( x - 2 )}{6} > \frac{( x + 3 )}{2} - 1

\frac{1 - 2 x}{3} + \frac{x - 2}{6} > \frac{x + 3}{2} - 1

Multiply by LCM

2 (- 2 x + 1) + x - 2 > 3 (x + 3) - 6

Expand

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

Expand

3 (x + 3) - 6 : 3 x + 3

- 3 x > 3 x + 3

Move

3 x

to the left side

- 6 x > 3

Multiply both sides by

- 1

6 x < - 3

Divide both sides by

6

x < - \frac{1}{2}

4 (2 x - 3) > 2 (x - 1)

\frac{( x + 3 )}{3} + \frac{( x + 2 )}{5} \geq \frac{( 7 x - 1 )}{15}

x - 2 < 0

\frac{( 2 x - 1 )}{5} - \frac{( 3 x + 1 )}{3} > \frac{( x - 5 )}{10}

20 x + 8 > 12 x + 16

What is ((1-2x))/3+((x-2))/6 >((x+3))/2-1 ?
The solution to ((1-2x))/3+((x-2))/6 >((x+3))/2-1 is x<-1/2