3<2x-1<= 9 — step-by-step solution

1) We have the following 2 conditions:

[1]:

3 < 2 x - 1

[2]:

2 x - 1 \leq 9

2) Let's solve for x:

3 < 2 x - 1

[1]

2 x - 1 > 3

ⓘ We add

1

to both sides

2 x > 3 + 1

ⓘ Start from

3

and move forward

1

on the number line:

3 + 1

4

2 x > 4

ⓘ Both sides are divided by

2

x > \frac{4}{2}

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

2

, their greatest common divisor:

\frac{4}{2}

2

Solution obtained [1]:

x > 2

3) Solving for x:

2 x - 1 \leq 9

[2] where

x > 2

2 x - 1 \leq 9

ⓘ We add

1

to both sides

2 x \leq 9 + 1

ⓘ Start from

9

and move forward

1

on the number line:

9 + 1

10

2 x \leq 10

ⓘ Both sides are divided by

2

x \leq \frac{10}{2}

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

2

, their greatest common divisor:

\frac{10}{2}

5

Solution found [2]:

x \leq 5

Intersecting

x > 2

and

x \leq 5

gives

x \in (2, 5]

▶Solution:

x \in (2, 5]