### Home > AC > Chapter 4 > Lesson 4.1.5 > Problem4-45

4-45.

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

1. $3p − 7 + 9 − 2p = p + 2$

2. $−2x + 5 + \left(−x\right) − 5 = 0$

3. $12 = r + 6 − 2r$

4. $−\left(y^{2} − 2\right) = y^{2} − 5 − 2y^{2}$

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.

\begin{align*} 3p + \left(−7\right) + 9 + \left(−2p\right) &= p + 2 \\ p + 2 &= p + 2 \\ p &= p \end{align*}

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.
$−y² + 2 = y² + −5 + −2y²$

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

\begin{align*} −y² + 2 &= −y² + −5 \\ 2 &= -5 \end{align*}

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