-1<2x-1<= 7 — step-by-step solution

1) We have the following 2 conditions:

[1]:

-1 < 2 x - 1

[2]:

2 x - 1 \leq 7

2) Let's solve for x:

-1 < 2 x - 1

[1]

3) Let's calculate:

2 x - 1 + 1 > 0

ⓘ Start from

-1

and move forward

1

on the number line, up to zero:

- 1 + 1

0

2 x + 0 > 0

ⓘ Adding 0 changes nothing:

2 x + 0

2 x

2 x > 0

We simplify the expression by

2

⇥Solution obtained [1]:

x > 0

4) Solving for x:

2 x - 1 \leq 7

[2] where

x > 0

2 x - 1 \leq 7

ⓘ We add

1

to both sides

2 x \leq 7 + 1

ⓘ Start from

7

and move forward

1

on the number line:

7 + 1

8

2 x \leq 8

ⓘ Both sides are divided by

2

x \leq \frac{8}{2}

ⓘ We simplify the fraction by dividing the numerator and the denominator by

2

, their greatest common divisor:

\frac{8}{2}

4

Solution obtained [2]:

x \leq 4

Intersecting

x > 0

and

x \leq 4

gives

x \in (0, 4]

▶Solution:

x \in (0, 4]