-10<= 5+x<-5 — step-by-step solution | Explain MAths

-10<= 5+x<-5

1) We have the following 2 conditions:

[1]:

-10 \leq 5 + x

[2]:

5 + x < -5

2) Let's solve for x:

-10 \leq 5 + x

[1]

5 + x \geq -10

ⓘ We subtract

5

from both sides

x \geq - 10 - 5

ⓘ Start from

-10

and move back

5

more on the number line, away from zero:

- 10 - 5

=

-15

Solution obtained [1]:

x \geq -15

3) Solving for x:

5 + x < -5

[2] using

x \geq -15

5 + x < -5

ⓘ We subtract

5

from both sides

x < - 5 - 5

ⓘ Start from

-5

and move back

5

more on the number line, away from zero:

- 5 - 5

=

-10

Solution found [2]:

x < -10

Intersecting

x \geq -15

and

x < -10

gives

x \in [-15, -10)

▶Solution:

x \in [-15, -10)