2(3-7x)+3x<3(5+2x) — step-by-step solution

Let's solve in

ℝ

2 \cdot (3 - 7 x) + 3 x < 3 \cdot (5 + 2 x)

ⓘ Expand by multiplying each term inside the parentheses:

2 \cdot (3 - 7 x)

6 - 14 x

3 \cdot (5 + 2 x)

15 + 6 x

6 - 14 x + 3 x < 15 + 6 x

ⓘ Like terms are grouped by adding their coefficients:

- 14 x + 3 x

-11 x

6 - 11 x < 15 + 6 x

ⓘ We gather the terms in

x

on the right and the other terms on the left

6 - 15 < 6 x + 11 x

ⓘ Start from

6

and move back

15

on the number line, going below zero:

6 - 15

-9

■Like terms are grouped by adding their coefficients:

6 x + 11 x

17 x

-9 < 17 x

ⓘ Both sides are divided by

17

▶Solution found:

x > - \frac{9}{17}

The numeric value of:

x > - \frac{9}{17}

equals:

▷

x > -0.5294 (approximate value)