10>-2x+4>-4 — step-by-step solution

1) We have the following 2 conditions:

[1]:

10 > - 2 x + 4

[2]:

- 2 x + 4 > -4

2) Solving for x:

10 > - 2 x + 4

[1]

- 2 x + 4 < 10

ⓘ We gather the terms in

x

on the right and the other terms on the left

4 - 10 < 2 x

ⓘ Start from

4

and move back

10

on the number line, going below zero:

4 - 10

-6

-6 < 2 x

ⓘ Both sides are divided by

2

x > - \frac{6}{2}

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

2

, their greatest common divisor:

- \frac{6}{2}

-3

Solution found [1]:

x > -3

3) Solving for x:

- 2 x + 4 > -4

[2] where

x > -3

- 2 x + 4 > -4

ⓘ We gather the terms in

x

on the right and the other terms on the left

4 + 4 > 2 x

ⓘ Start from

4

and move forward

4

on the number line:

4 + 4

8

8 > 2 x

ⓘ Both sides are divided by

2

x < \frac{8}{2}

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

2

, their greatest common divisor:

\frac{8}{2}

4

Solution found [2]:

x < 4

Intersecting

x > -3

and

x < 4

gives

x \in (-3, 4)

▶Solution:

x \in (-3, 4)