How do you solve #abs(2y-5)

Question

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

Kennedy Adams · Accepted Answer

undefined To solve the inequality $ |2y - 5| \leq 3 $, you consider two cases:

Case 1: $ 2y - 5 \geq 0 $
$$ 2y - 5 \leq 3 $$

Case 2: $ 2y - 5 < 0 $
$$ -(2y - 5) \leq 3 $$

Solve each inequality separately to find the possible values of y for each case. Then, combine the solutions to determine the overall solution set for the original inequality.

Avery Alexander · Answer

See a solution process below:

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]#

How do you solve #abs(2y-5)&lt;=3#?

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