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

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

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

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

x \leq - 2

Interval Notation

(- \infty, - 2]

Solution steps

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

Expand

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

Expand

\frac{3}{4} (x - 6) + 1 : - \frac{7}{2} + \frac{3}{4} x

\frac{3}{2} x - 2 \leq - \frac{7}{2} + \frac{3}{4} x

Move

2

to the right side

\frac{3}{2} x \leq - \frac{3}{2} + \frac{3}{4} x

Move

\frac{3}{4} x

to the left side

\frac{3}{4} x \leq - \frac{3}{2}

Multiply both sides by

4

3 x \leq - 6

Divide both sides by

3

x \leq - 2

x (\frac{1}{2} x^{- \frac{1}{2}})

c + 9 - 3 (c - 10) > 1

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

x + \frac{1}{x} \geq 1

4 x y + 12 y - 4 x - 12

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