What is 4x+3(x-1)<= 5x+(1-2x) ?

The solution to 4x+3(x-1)<= 5x+(1-2x) is x<= 1

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4x+3(x-1)<= 5x+(1-2x)

4 x + 3 (x - 1) \leq 5 x + (1 - 2 x)

x \leq 1

Interval Notation

(- \infty, 1]

Solution steps

4 x + 3 (x - 1) \leq 5 x + (1 - 2 x)

Remove parentheses:

(a) = a

4 x + 3 (x - 1) \leq 5 x + 1 - 2 x

Group like terms

4 x + 3 (x - 1) \leq 5 x - 2 x + 1

Add similar elements:

5 x - 2 x = 3 x

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

Expand

3 (x - 1) : 3 x - 3

4 x + 3 x - 3 \leq 3 x + 1

Add similar elements:

4 x + 3 x = 7 x

7 x - 3 \leq 3 x + 1

Move

3

to the right side

7 x \leq 3 x + 4

Move

3 x

to the left side

4 x \leq 4

Divide both sides by

4

x \leq 1

2 - 2 x < 4 x - 8

x - 5 > 7

2 x + 1 > 41

3 x - 5 < - 2

5 \frac{x}{5} - \frac{13}{21} + \frac{x}{15} < \frac{9}{25} - 2 \frac{x}{35}