-1<= x-3<4 — step-by-step solution | Explain MAths

-1<= x-3<4

1) We have the following 2 conditions:

[1]:

-1 \leq x - 3

[2]:

x - 3 < 4

2) Let's solve for x:

-1 \leq x - 3

[1]

x - 3 \geq -1

ⓘ We add

3

to both sides

x \geq - 1 + 3

ⓘ Start from

-1

and move forward

3

on the number line, going past zero:

- 1 + 3

=

2

Solution obtained [1]:

x \geq 2

3) Let's solve for x:

x - 3 < 4

[2] where

x \geq 2

x - 3 < 4

ⓘ We add

3

to both sides

x < 4 + 3

ⓘ Start from

4

and move forward

3

on the number line:

4 + 3

=

7

Solution found [2]:

x < 7

Intersecting

x \geq 2

and

x < 7

gives

x \in [2, 7)

▶Solution:

x \in [2, 7)