Find all solutions x of the inequality
5/24 + |x - 1/3| < 5/16.
Express your answer in interval notation, simplifying all fractions in your answer.
5/24 + l x - 1/3 l < 5/16 subtract 3/24 from both sides
l x - 1/3 l < 5/16 - 5/24 get a common denominator (48) on the right
l x - 1/3 l < 15/48 - 10/48
l x - 1/3 l < 5/48
We have two equations here
x - 1/3 < 5/48 x - 1/3 > -5 / 48
add 1/3 to both sides
x < 5/48 + 1/3 x > -5/48 + 1/3
x < 5/48 + 16/48 x > -5/48 + 16/48
x < 21/48 x > 11/48
x < 7/16
So the solution is 11/48 < x < 7/16
Convert entire equation to common denominator 48
10/48 + |x-16/48| < 15/48 subtract 10/48 from both sides of the equation
|x-16/48| < 5/48 now solve the following
x -16/48 < 5/48 or x - 16/48 > 5/48
x < 21/48 x > 21/48 you should be able to take it from here....
5/24 + l x - 1/3 l < 5/16 subtract 3/24 from both sides
l x - 1/3 l < 5/16 - 5/24 get a common denominator (48) on the right
l x - 1/3 l < 15/48 - 10/48
l x - 1/3 l < 5/48
We have two equations here
x - 1/3 < 5/48 x - 1/3 > -5 / 48
add 1/3 to both sides
x < 5/48 + 1/3 x > -5/48 + 1/3
x < 5/48 + 16/48 x > -5/48 + 16/48
x < 21/48 x > 11/48
x < 7/16
So the solution is 11/48 < x < 7/16