4-2x>-4x+2>=-2x-2 — step-by-step solution

1) We have the following 2 conditions:

[1]:

4 - 2 x > - 4 x + 2

[2]:

- 4 x + 2 \geq - 2 x - 2

2) Solving for x:

4 - 2 x > - 4 x + 2

[1]

4 - 2 x > - 4 x + 2

ⓘ We subtract

4

from both sides■Start from

2

and move back

4

on the number line, going below zero:

2 - 4

-2

- 2 x > - 4 x - 2

ⓘ We add

4 x

to both sides

- 2 x + 4 x > -2

ⓘ Like terms are grouped by adding their coefficients:

- 2 x + 4 x

2 x

2 x > -2

ⓘ Both sides are divided by

2

x > - \frac{2}{2}

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

2

, their greatest common divisor:

- \frac{2}{2}

-1

Solution obtained [1]:

x > -1

3) Let's solve for x:

- 4 x + 2 \geq - 2 x - 2

[2] where

x > -1

- 4 x + 2 \geq - 2 x - 2

ⓘ We gather the terms in

x

on the right and the other terms on the left

2 + 2 \geq - 2 x + 4 x

ⓘ Start from

2

and move forward

2

on the number line:

2 + 2

4

■Like terms are grouped by adding their coefficients:

- 2 x + 4 x

2 x

4 \geq 2 x

ⓘ Both sides are divided by

2

x \leq \frac{4}{2}

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

2

, their greatest common divisor:

\frac{4}{2}

2

Solution obtained [2]:

x \leq 2

Intersecting

x > -1

and

x \leq 2

gives

x \in (-1, 2]

▶Solution:

x \in (-1, 2]