What is 1/3 x+2/5 x-1/2 (x-3)<= 1/10 ?

The solution to 1/3 x+2/5 x-1/2 (x-3)<= 1/10 is x<=-6

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1/3 x+2/5 x-1/2 (x-3)<= 1/10

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

x \leq - 6

Interval Notation

(- \infty, - 6]

Solution steps

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

Multiply by LCM

22 x - 15 (x - 3) \leq 3

Expand

- 15 (x - 3) : - 15 x + 45

22 x - 15 x + 45 \leq 3

Add similar elements:

22 x - 15 x = 7 x

7 x + 45 \leq 3

Move

45

to the right side

7 x \leq - 42

Divide both sides by

7

x \leq - 6

6 x^{2} - 19 x + 10 = 0

3 x^{2} = 2

x^{2} = 4 - x

- 70

4^{5}

What is 1/3 x+2/5 x-1/2 (x-3)<= 1/10 ?
The solution to 1/3 x+2/5 x-1/2 (x-3)<= 1/10 is x<=-6