### Home > CC3MN > Chapter 4 > Lesson 4.1.5 > Problem4-51

4-51.

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

1. $3p−7+9−2p=p+2$, solve for $p$

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

$3p+(−7)+9+(−2p)=p+2$
$p+2=p+2$
$p=p$

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

1. $−2x+5+(−x)−5=0$, solve for $x$

Refer to parts (a) and (d).

1. $12=r+6−2r$, solve for $r$

Refer to parts (a) and (d).

1. $−(y^2−2)=y^2−5−2y^2$, solve for $y$

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

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

$−y^2+2=−y^2+−5$
$2=−5$

No solution because $2$ is not equal to $−5$.