-4x-23>= 2-3(3+2x) — step-by-step solution

Let's solve in

ℝ

- 4 x - 23 \geq 2 - 3 \cdot (3 + 2 x)

ⓘ Expand by multiplying each term inside the parentheses:

- 3 \cdot (3 + 2 x)

- (9 + 6 x)

- 4 x - 23 \geq 2 - (9 + 6 x)

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

- (9 + 6 x)

- 9 - 6 x

- 4 x - 23 \geq 2 - 9 - 6 x

ⓘ Start from

2

and move back

9

on the number line, going below zero:

2 - 9

-7

- 4 x - 23 \geq - 7 - 6 x

ⓘ We add

23

to both sides■Start from

-7

and move forward

23

on the number line, going past zero:

- 7 + 23

16

- 4 x \geq 16 - 6 x

ⓘ We add

6 x

to both sides

- 4 x + 6 x \geq 16

ⓘ Like terms are grouped by adding their coefficients:

- 4 x + 6 x

2 x

2 x \geq 16

ⓘ Both sides are divided by

2

x \geq \frac{16}{2}

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

2

, their greatest common divisor:

\frac{16}{2}

8

▶Solution found:

x \geq 8