-5<2x+3<= 5 — step-by-step solution

1) You have the following 2 equations:

[1]:

-5 < 2 x + 3

[2]:

2 x + 3 <= 5

2) Let's solve for x:

-5 < 2 x + 3

[1]

2 x + 3 > -5

2 x > - 5 - 3

2 x > -8

You can write the expression in factored form:

2 \cdot (x + 4) > 0

3) Let's solve:

x + 4 > 0

[1]

Solution obtained [1]:

x > -4

4) Let's solve for x:

2 x + 3 <= 5

[2] where

x > -4

2 x + 3 <= 5

2 x <= 5 - 3

2 x <= 2

You can factorize this expression into:

2 \cdot (x - 1) <= 0

5) Let's solve:

x - 1 <= 0

[2]

Solution obtained [2]:

x <= 1

Let's aggregate the different solutions to find the overall solution:

▶Solution obtained [2]:

x \in (-4, 1]