Question

8-2|4-5y|=4 | | stands for absolute value

Answer 1

Answer:

y = (2/5) OR y = (6/5)

Step-by-step explanation:

The first step is isolating the expression within the absolute value bars. The first thing we can do is subtract both sides by 8. If we do that, we get -2|4-5y| = -4. Now, to completely isolate the absolute value, we would have to divide by -2. This yields |4 - 5y| = 2. Finally, we can remove the absolute value bars. However, to do this, we need to first understand what an absolute value bar does to an equation. Lets say that |x| = 2. Absolute value describes the DISTANCE of some quantity from 0 (on the number line). Therefore, x (which is inside the absolute value bars) can be either positive or negative 2 (they are BOTH two units away from 0). Similarly, in this case, (4 - 5y) can either be 2 or -2 (because the absolute value of both is 2). Now we have two possible solutions to solve for:

4 - 5y = 2 OR 4 - 5y = -2

5y = 2 OR 5y = 6

y = (2/5) OR y = (6/5)

If we plug both of these answers back into the equation we can see that they both check out.