-3<= x-2<4 — step-by-step solution | Explain MAths

-3<= x-2<4

1) We have the following 2 conditions:

[1]:

-3 \leq x - 2

[2]:

x - 2 < 4

2) Solving for x:

-3 \leq x - 2

[1]

x - 2 \geq -3

ⓘ We add

2

to both sides

x \geq - 3 + 2

ⓘ Start from

-3

and move forward

2

on the number line, getting closer to zero:

- 3 + 2

=

-1

Solution obtained [1]:

x \geq -1

3) Solving for x:

x - 2 < 4

[2] where

x \geq -1

x - 2 < 4

ⓘ We add

2

to both sides

x < 4 + 2

ⓘ Start from

4

and move forward

2

on the number line:

4 + 2

=

6

Solution obtained [2]:

x < 6

Intersecting

x \geq -1

and

x < 6

gives

x \in [-1, 6)

▶Solution:

x \in [-1, 6)