-9d-4(-3d-3)>= 6d+6+6d — step-by-step solution

Let's solve in

ℝ

- 9 d - 4 \cdot (- 3 d - 3) \geq 6 d + 6 + 6 d

ⓘ Like terms are grouped by adding their coefficients:

6 d + 6 d

12 d

- 9 d - 4 \cdot (- 3 d - 3) \geq 12 d + 6

ⓘ Expand by multiplying each term inside the parentheses:

- 4 \cdot (- 3 d - 3)

- (- 12 d - 12)

- 9 d - (- 12 d - 12) \geq 12 d + 6

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

- (- 12 d - 12)

12 d + 12

- 9 d + 12 d + 12 \geq 12 d + 6

ⓘ Like terms are grouped by adding their coefficients:

- 9 d + 12 d

3 d

3 d + 12 \geq 12 d + 6

ⓘ We gather the terms in

d

on the right and the other terms on the left

12 - 6 \geq 12 d - 3 d

ⓘ Start from

12

and move back

6

on the number line:

12 - 6

6

■Like terms are grouped by adding their coefficients:

12 d - 3 d

9 d

6 \geq 9 d

ⓘ Both sides are divided by

9

d \leq \frac{6}{9}

ⓘ We simplify the fraction by dividing the numerator and the denominator by

3

, their greatest common divisor:

\frac{6}{9}

\frac{2 \cdot 3}{3 \cdot 3}

\frac{2}{3}

▶Solution obtained:

d \leq \frac{2}{3}

The numeric value of:

d \leq \frac{2}{3}

equals:

▷

d \leq 0.6667 (approximate value)