CAHSEE practice: Problems 52-53

Problem 52. Colleen solved the equation 2 times 2x plus 5 is equal to 8 using the following steps. OK, so she has a bunch of steps. To get from Step 2 to Step 3, Colleen-- so it's good that I read the question before I just started diving into it. So to get from Step 2 to Step 3-- so this is her Step 2, and this is her Step 3 right here. What did she do to get from here to here? Well, she divided both sides by 4. Right? You could say 4x is equal to minus 2. If you divide both sides of this equation by 4, the left-hand side-- these cancel out, you're just left with x. And then the right-hand side, minus 2/4 is just minus 1/2. So she just divided both sides by 4. And that is choice A. She definitely didn't subtract 4 from both sides. She didn't add 4 to both sides. And she didn't multiply both sides by 4. Then we would have had 16x minus 8. So that was a pretty straightforward problem. And then 53. What is the reciprocal of ax squared over y? This is another, you just have to know what a reciprocal is. A reciprocal of something is just 1 over that something. Or if it's a fraction, you just flip it. So if you have a/b, the reciprocal is b/a. If you have xy/ab, the reciprocal is going to be ab/xy. So if you have ax squared over y, its reciprocal is just going to be y over ax squared. That easy. And that is choice D, y over ax squared. You just have to know to flip this fraction right there.