CPM Homework Help : AC Problem 4-45

For each equation below, solve for the variable. Check your solutions, if possible, and show all work. Homework Help ✎
1. 3p − 7 + 9 − 2p = p + 2
2. −2x + 5 + (−x) − 5 = 0
3. 12 = r + 6 − 2r
4. −(y² − 2) = y² − 5 − 2y²

For more help with parts (a) - (d), see the equation mat in problem 2-105.

Hint (a):

First, try rewriting all of the subtraction as addition, then attempt to solve by simplifying like terms.

3p + (−7) + 9 + (−2p) = p + 2
p + 2 = p + 2
p = p

Answer (a):

Since p = p (or 2 = 2, depending on how you solved the problem),
p can equal any number.

Hint (d):

One strategy is to rewrite all of the subtraction within the problem as addition.
−y² + 2 = y² + −5 + −2y²

More Help (d):

Now simplify, starting with combining like terms and then with isolating the variable.

−y² + 2 = −y² + −5
2 = −5

Answer (d):

No solution because 2 is not equal to −5.