2(x-2)+3x<5x+6 — step-by-step solution

Let's solve in

ℝ

2 \cdot (x - 2) + 3 x < 5 x + 6

2 \cdot (x - 2)

+ 3 x

- 5 x

- 6 < 0

ⓘ Like terms are grouped by adding their coefficients:

3 x - 5 x

-2 x

2 \cdot (x - 2) - 2 x - 6 < 0

ⓘ Expand by multiplying each term inside the parentheses:

2 \cdot (x - 2)

2 x - 4

2 x

- 4

- 2 x

- 6 < 0

ⓘ Start from

-4

and move back

6

more on the number line, away from zero:

- 4 - 6

-10

■Like terms are grouped by adding their coefficients:

2 x - 2 x

0

0 - 10 < 0

ⓘ Adding 0 changes nothing:

0 - 10

-10

-10 < 0

▶Solution obtained:

x \in ℝ