-1/4 (12x+8)<=-2x+11 — step-by-step solution

⚠ -1/4 (12x+8)<=-2x+11 is read as -(1/4)*(12x+8)<=-2x+11: use (-1/4)*(12x+8) to multiply by the following factor, use -1/(4*(12x+8)) to include it in the denominator

Let's solve in

ℝ

- \frac{1}{4} \cdot (12 x + 8) \leq - 2 x + 11

ⓘ Expand by multiplying each term inside the parentheses:

- \frac{1}{4} \cdot (12 x + 8)

- (3 x + 2)

- (3 x + 2) \leq - 2 x + 11

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

- (3 x + 2)

- 3 x - 2

- 3 x - 2 \leq - 2 x + 11

ⓘ We gather the terms in

x

on the right and the other terms on the left

- 2 - 11 \leq - 2 x + 3 x

ⓘ Start from

-2

and move back

11

more on the number line, away from zero:

- 2 - 11

-13

■Like terms are grouped by adding their coefficients:

- 2 x + 3 x

x

-13 \leq x

▶Solution found:

x \geq -13