4x-3(5x-9+2(-x+1))>=0 — step-by-step solution

Let's solve in

ℝ

4 x - 3 \cdot (5 x - 9 + 2 \cdot (- x + 1)) \geq 0

ⓘ Expand by multiplying each term inside the parentheses:

2 \cdot (- x + 1)

2 \cdot (- x) + 2

- 3 \cdot (5 x - 9 + (2 \cdot (- x) + 2))

- (15 x - 27 + 3 \cdot (2 \cdot (- x) + 2))

4 x - (15 x - 27 + 3 \cdot (2 \cdot (- x) + 2)) \geq 0

ⓘ A minus sign before a parenthesis changes the sign of each of its terms:

- (15 x - 27 + 3 \cdot (2 \cdot (- x) + 2))

- 15 x + 27 - 3 \cdot (2 \cdot (- x) + 2)

4 x

- 15 x

+ 27

- 3 \cdot (2 \cdot (- x) + 2) \geq 0

ⓘ Like terms are grouped by adding their coefficients:

4 x - 15 x

-11 x

■The minus sign is placed in front of the product:

2 \cdot (- x)

- 2 x

- 11 x + 27 - 3 \cdot (- 2 x + 2) \geq 0

ⓘ Expand by multiplying each term inside the parentheses:

- 3 \cdot (- 2 x + 2)

- (- 6 x + 6)

- 11 x + 27 - (- 6 x + 6) \geq 0

ⓘ A minus sign before a parenthesis changes the sign of each of its terms:

- (- 6 x + 6)

6 x - 6

- 11 x

+ 27

+ 6 x

- 6 \geq 0

ⓘ Start from

27

and move back

6

on the number line:

27 - 6

21

■Like terms are grouped by adding their coefficients:

- 11 x + 6 x

-5 x

- 5 x + 21 \geq 0

ⓘ We add

5 x

to both sides

21 \geq 5 x

ⓘ Both sides are divided by

5

▶Solution obtained:

x \leq \frac{21}{5}

The numeric value of:

x \leq \frac{21}{5}

is:

▷

x \leq 4.2