x-1<= 2x+4<= 3x-1 — step-by-step solution

1) We have the following 2 conditions:

[1]:

x - 1 \leq 2 x + 4

[2]:

2 x + 4 \leq 3 x - 1

2) Let's solve for x:

x - 1 \leq 2 x + 4

[1]

x - 1 \leq 2 x + 4

ⓘ We gather the terms in

x

on the right and the other terms on the left

- 1 - 4 \leq 2 x - x

ⓘ Start from

-1

and move back

4

more on the number line, away from zero:

- 1 - 4

-5

■Like terms are grouped by adding their coefficients:

2 x - x

x

-5 \leq x

Solution found [1]:

x \geq -5

3) Solving for x:

2 x + 4 \leq 3 x - 1

[2] where

x \geq -5

2 x + 4 \leq 3 x - 1

ⓘ We gather the terms in

x

on the right and the other terms on the left

4 + 1 \leq 3 x - 2 x

ⓘ Start from

4

and move forward

1

on the number line:

4 + 1

5

■Like terms are grouped by adding their coefficients:

3 x - 2 x

x

5 \leq x

Solution obtained [2]:

x \geq 5

Intersecting

x \geq -5

and

x \geq 5

gives

x \geq 5

▶Solution:

x \geq 5