Final answer:
To solve (2x-4)/(x+1)≤1, we simplify the inequality to (x-5)/(x+1)≤0 and find intervals where the inequality holds by setting up a sign chart around the critical points x = 5 and x = -1.
Step-by-step explanation:
To solve the inequality (2x-4)/(x+1)≤1, we first need to bring all terms to one side of the inequality so that we can compare it to zero. This gives us (2x-4)/(x+1) - 1 ≤ 0. Simplifying this, we get (2x-4-x-1)/(x+1) ≤ 0, which simplifies further to (x-5)/(x+1) ≤ 0. Now the inequality is set up such that we can find the intervals for x where the inequality holds true.
To find the intervals where the inequality holds true, we set up a sign chart and determine where the expression is positive or negative. We find that the critical points are x = 5 and x = -1. Testing points in each interval, we determine which intervals satisfy the original inequality.
The solution set is then all x-values in the intervals that make the inequality true, taking into consideration the critical points where the inequality may not be defined or changes its sign.