How do you solve the compound inequality 3<2x-3<15?

2 Answers
May 21, 2017

See a solution process below:

Explanation:

First, add color(red)(3) to each segment of the system of inequalities to isolate the x term while keeping the system balanced:

3 + color(red)(3) < 2x - 3 + color(red)(3) < 15 + color(red)(3)

6 < 2x - 0 < 18

6 < 2x < 18

Now, divide each segment by color(red)(2) to solve for x while keeping the system balanced:

6/color(red)(2) < (2x)/color(red)(2) < 18/color(red)(2)

3 < (color(red)(cancel(color(black)(2)))x)/cancel(color(red)(2)) < 9

3 < x < 9

Or

x > 3; x < 9

Or, in interval notation:

(3, 9)

May 21, 2017

Solution: 3 < x < 9 or in interval notation: (3,9)

Explanation:

3 < 2x-3 <15 Adding 3 in all sides we get

6 < 2x <18 Multiplying by 1/2 in all sides we get

3 < x < 9 .

Solution: 3 < x < 9 or in interval notation: (3,9) [Ans]