What is (3-2(x-2))/6-(1+3(2-x))/4 <=-(3x-1)/(12) ?

The solution to (3-2(x-2))/6-(1+3(2-x))/4 <=-(3x-1)/(12) is x<= 1

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(3-2(x-2))/6-(1+3(2-x))/4 <=-(3x-1)/(12)

\frac{3 - 2 ( x - 2 )}{6} - \frac{1 + 3 ( 2 - x )}{4} \leq - \frac{3 x - 1}{12}

x \leq 1

Interval Notation

(- \infty, 1]

Solution steps

\frac{3 - 2 ( x - 2 )}{6} - \frac{1 + 3 ( 2 - x )}{4} \leq - \frac{3 x - 1}{12}

Multiply by LCM

2 (- 2 (x - 2) + 3) - 3 (3 (- x + 2) + 1) \leq - (3 x - 1)

Expand

2 (- 2 (x - 2) + 3) - 3 (3 (- x + 2) + 1) : 5 x - 7

Expand

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

5 x - 7 \leq - 3 x + 1

Move

7

to the right side

5 x \leq - 3 x + 8

Move

3 x

to the left side

8 x \leq 8

Divide both sides by

8

x \leq 1

∣ 4 x - 2 ∣ = ∣ x - 1 ∣

2 x^{2} + 3 + 4 x^{3} + 1

x^{2} + 4 x - 12

- 4 a^{2} - 12 a + 40 = - 4 (a + 5) (a - 2)

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

What is (3-2(x-2))/6-(1+3(2-x))/4 <=-(3x-1)/(12) ?
The solution to (3-2(x-2))/6-(1+3(2-x))/4 <=-(3x-1)/(12) is x<= 1