Question

Solve the compound inequality.

5 < 2x - 1<9

show your work solving the inequality

Answer 1

`x = (5 \: . \: 3)`

Explanation:

To solve a compound inequality, seperate it into two inequalities:

`2x - 1 > 5 \\ 2x - 1 < 9`

Solve the inequality for x:

`x > 3 \\ 2x - 1 < 9`

Solve the inequality for x:

`x > 3 \\ x < 5`

Find the intersection:

`x = (5 \: . \: 3)`

Answer 2

x> 3 and x <5

OR

3 < x <5

Explanation:

To solve the compound inequality, we will follow the steps below:

We will first break it into two inequalities.

That is;

5 < 2x - 1<9

5 < 2x - 1 AND 2x - 1<9

Then we will solve separately

5 < 2x - 1

add 1 to both-side of the equation

5 +1 < 2x - 1 +1

6 < 2x

Divide both-side of the inequality by 2

6 /2 < 2x/2

3 < x

x>3

we will now solve the other inequality

2x - 1<9

add 1 to both-side of the equation

2x - 1+1<9 +1

2x < 10

divide both-side of the inequality by 2

2x /2< 10/2

x < 5

Therefore x> 3 and x <5

or

3 < x <5