What is (3x+1)/4-1/3 <= 2/15 (3x+2)+(4(1-x))/3 ?

The solution to (3x+1)/4-1/3 <= 2/15 (3x+2)+(4(1-x))/3 is x<= 1

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(3x+1)/4-1/3 <= 2/15 (3x+2)+(4(1-x))/3

\frac{3 x + 1}{4} - \frac{1}{3} \leq \frac{2}{15} (3 x + 2) + \frac{4 ( 1 - x )}{3}

x \leq 1

Interval Notation

(- \infty, 1]

Solution steps

\frac{3 x + 1}{4} - \frac{1}{3} \leq \frac{2}{15} (3 x + 2) + \frac{4 ( 1 - x )}{3}

Multiply by LCM

15 (3 x + 1) - 20 \leq 8 (3 x + 2) + 80 (- x + 1)

Expand

15 (3 x + 1) - 20 : 45 x - 5

Expand

8 (3 x + 2) + 80 (- x + 1) : - 56 x + 96

45 x - 5 \leq - 56 x + 96

Move

5

to the right side

45 x \leq - 56 x + 101

Move

56 x

to the left side

101 x \leq 101

Divide both sides by

101

x \leq 1

- 2 - 3 n = - 56

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

1 > \frac{- 7 x + 3}{4} \geq - 6

100 - 9 x^{2}

\frac{1}{4} x + 3 \geq - \frac{3}{4} x + 11

What is (3x+1)/4-1/3 <= 2/15 (3x+2)+(4(1-x))/3 ?
The solution to (3x+1)/4-1/3 <= 2/15 (3x+2)+(4(1-x))/3 is x<= 1