Question

Solve the inequality: -2|y-3|-5 ≤ -4

A) y ≥ 1
B) y ≤ 1
C) y ≥ 2
D) y ≤ 2

Answer 1

To solve the inequality -2|y-3|-5 ≤ -4, isolate the absolute value term, simplify the inequality, and solve for y. The solution is y ≥ 3.

Step-by-step explanation:

To solve the inequality -2|y-3|-5 ≤ -4, we can start by isolating the absolute value term. First, add 5 to both sides of the equation to get -2|y-3| ≤ 1. Next, divide both sides of the equation by -2 to get |y-3| ≥ -0.5. Since the absolute value of any number is always greater than or equal to 0, we can simplify the inequality to y-3 ≥ -0.5.

Now, we can solve for y by adding 3 to both sides of the inequality. This gives us y ≥ 2.5. However, since y represents a real number, we can't have a half value, so we can round up to the next whole number. Therefore, the solution to the inequality is y ≥ 3.

Option C) y ≥ 2 is the correct answer.