Answer:
y = -3x -4
Step-by-step explanation:
Any "solve for" problem involves inverse operations. You want to "undo" what has been done to the variable of interest. Generally, we're undoing multiplication or addition.
__
It can help to simplify the equation first:
x -(y +2) = 2(2x +1)
x -y -2 = 4x +2 . . . . eliminate parentheses using the distributive property
To get y by itself, we can undo the addition of (x -2) by subtracting that from both sides.
-y = (4x +2) -(x -2)
-y = 3x +4
To "undo" the multiplication of y by -1, we can multiply by the reciprocal of that, which is -1.
(-y)(-1) = (-1)(3x +4)
y = -3x -4
__
<em>Additional comment</em>
Here, we simplified the equation first. That's not always necessary or desirable. <em>The first step is to look at what you have and make a plan</em>. Here, y is in parentheses, so part of the plan will be to eliminate those parentheses.
