-44>-2x-8>=-8 — step-by-step solution

1) We have the following 2 conditions:

[1]:

-44 > - 2 x - 8

[2]:

- 2 x - 8 \geq -8

2) Let's solve for x:

-44 > - 2 x - 8

[1]

- 2 x - 8 < -44

ⓘ We gather the terms in

x

on the right and the other terms on the left

- 8 + 44 < 2 x

ⓘ Start from

-8

and move forward

44

on the number line, going past zero:

- 8 + 44

36

36 < 2 x

ⓘ Both sides are divided by

2

x > \frac{36}{2}

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

2

, their greatest common divisor:

\frac{36}{2}

18

Solution found [1]:

x > 18

3) Solving for x:

- 2 x - 8 \geq -8

[2] using

x > 18

- 2 x - 8 + 8 \geq 0

ⓘ Start from

-8

and move forward

8

on the number line, up to zero:

- 8 + 8

0

- 2 x + 0 \geq 0

ⓘ Adding 0 changes nothing:

- 2 x + 0

- 2 x

- 2 x \geq 0

We simplify the expression by

-2

and since

-2

is negative, we reverse the inequality sign

⇥Solution obtained [2]:

x \leq 0

No value of

x

satisfies both

x > 18

and

x \leq 0

▶Solution:

\emptyset