What is ((5x-3))/6+((x-5)}{18}<\frac{(x+1))/3 ?

The solution to ((5x-3))/6+((x-5)}{18}<\frac{(x+1))/3 is x<2

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((5x-3))/6+((x-5)}{18}<\frac{(x+1))/3

\frac{( 5 x - 3 )}{6} + \frac{( x - 5 )}{18} < \frac{( x + 1 )}{3}

x < 2

Interval Notation

(- \infty, 2)

Solution steps

\frac{( 5 x - 3 )}{6} + \frac{( x - 5 )}{18} < \frac{( x + 1 )}{3}

\frac{5 x - 3}{6} + \frac{x - 5}{18} < \frac{( x + 1 )}{3}

Multiply by LCM

3 (5 x - 3) + x - 5 < 6 (x + 1)

Expand

3 (5 x - 3) + x - 5 : 16 x - 14

Expand

6 (x + 1) : 6 x + 6

16 x - 14 < 6 x + 6

Move

14

to the right side

16 x < 6 x + 20

Move

6 x

to the left side

10 x < 20

Divide both sides by

10

x < 2

- 4 x + 12 > 0

\frac{( 2 ( 3 x - 11 ) )}{3} \geq 14

x, y > 2 + 9 x

\frac{5}{6} x - \frac{1}{3} > \frac{11}{3}

x, - x + 3 y > - 12

What is ((5x-3))/6+((x-5)}{18}<\frac{(x+1))/3 ?
The solution to ((5x-3))/6+((x-5)}{18}<\frac{(x+1))/3 is x<2