How do you solve abs(2y-5)<=3?

1 Answer
Jul 5, 2017

See a solution process below:

Explanation:

The absolute value function takes any negative or positive term and transforms it to its positive form. Therefore, we must solve the term within the absolute value function for both its negative and positive equivalent.

-3 <= 2y - 5 <= 3

First, add color(red)(5) to each segment of the system of inequalities to isolate the y term while keeping the system balanced:

-3 + color(red)(5) <= 2y - 5 + color(red)(5) <= 3 + color(red)(5)

2 <= 2y - 0 = 8

2 <= 2y = 8

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

2/color(red)(2) <= (2y)/color(red)(2) = 8/color(red)(2)

1 <= (color(red)(cancel(color(black)(2)))y)/cancel(color(red)(2)) = 4

1 <= y = 4

Or

y >= 1 and y <= 4

Or, in interval notation:

[1, 4]