### Home > CAAC > Chapter 4 > Lesson 4.1.5 > Problem 4-45

For each equation below, solve for the variable. Check your solutions, if possible, and show all work. Homework Help ✎

3

*p*− 7 + 9 − 2*p*=*p*+ 2−2

*x*+ 5 + (−*x*) − 5 = 012 =

*r*+ 6 − 2*r*−(

*y*^{2}− 2) =*y*^{2}− 5 − 2*y*^{2}

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

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

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

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

One strategy is to rewrite all of the subtraction within the problem as addition.

− *y*^{2} + 2 = *y*^{2} + − 5 + −2*y*^{2}

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

−*y*^{2} + 2 = −*y*^{2} + −5

2 = −5

No solution because 2 is not equal to −5.