Equations with variables on both sides
Equations with variables on both sides - Questions
Answers
1. \(e=−2 \)
We need to manipulate the equation to get \(e\) by itself.
| \(9e−7=7e−11\) | |
| \(9 e-7-7 e=7 e-11-7 e\) | Subtract \(7e\) from each side. |
| \(2 e-7=-11\) | Combine like terms. |
| \(2 e-7+7=-11+7\) | Add \(7\) to each side. |
| \(2 e=-4\) | Combine like terms. |
| \(\frac{2 e}{2}=\frac{-4}{2}\) | Divide each side by \(2\). |
| \(e=-2\) | Simplify, |
The answer: \(e=−2 \)
Let's check our work!
\(\begin{gathered}
9 e-7=7 e-11 \\
9(-2)-7 \stackrel{?}{=} 7(-2)-11 \\
-18-7 \stackrel{?}{=}-14-11 \\
-25=-25 \quad \text { Yes! }
\end{gathered}\)
2. \(p = 2\)
We need to manipulate the equation to get \(p\) by itself.
| \(17−2p=2p+5+2p\) | |
| \(17-2 p =4 p+5 \) | Combine like terms. |
| \(17-2 p-4 p =4 p+5-4 p \) | Subtract \(4p\) from each side. |
| \(-6 p+17 =5 \) | Combine like terms. |
| \(-6 p+17-17 =5-17 \) | Subtract \(17\) from each side. |
| \(\frac{-6 p}{-6 p} =-12 \) | Combine like terms. |
| \(\frac{-6}{-6} =\frac{-12}{-6} \) | Divide each side by \(-6\) |
| \(p = 2\) | Simplify. |
The answer: \(p = 2\)
Let's check our work!
\(\begin{aligned}
17-2 p &=2 p+5+2 p \\
17-2 p &=4 p+5 \\
17-2(2) & \stackrel{?}{=} 4(2)+5 \\
17-4 & \stackrel{?}{=} 8+5 \\
13 &=13 \quad \text { Yes! }
\end{aligned}\)
3. \(a =-2 \)
We need to manipulate the equation to get \(a\) by itself.
| \(5+14a=9a−5\) | |
| \(5+14 a-9 a =9 a-5-9 a \) | Subtract \(9a\) from each side. |
| \(5+5 a =-5\) | Combine like terms. |
| \(5+5 a-5 =-5-5\) | Subtract \(5\) from each side. |
| \(5 a =-10\) | Combine like terms. |
| \(\frac{5 a}{5} =\frac{-10}{5} \) | Divide each side by \(5\). |
| \(a =-2 \) | Simplify. |
The answer: \(a =-2 \)
Let's check our work!
\(\begin{aligned}
5+14 a &=9 a-5 \\
5+14(-2) & \stackrel{?}{=} 9(-2)-5 \\
5+(-28) & \stackrel{?}{=}-18-5 \\
-23 &=-23 \quad \text { Yes! }
\end{aligned}\)
4. \(m = 2\)
We need to manipulate the equation to get \(m\) by itself.
| \(−7+4m+10=15−2m \) | |
| \( 4 m+3 =15-2 m \) | Combine like terms. |
| \( 3+4 m+2 m =15-2 m+2 m \) | Add \(2m\) to each side. |
| \( 6 m+3 =15 \) | Combine like terms. |
| \( 6 m+3-3 =15-3 \) | Subtract \(3\) from each side. |
| \( 6 m =12 \) | Combine like terms. |
| \( \frac{6 m}{6} =\frac{12}{6} \) | Divide each side by \(6\). |
| \( m = 2\) | Simplify. |
The answer: \(m = 2\)
Let's check our work!
\(\begin{aligned}
-7+4 m+10 &=15-2 m \\
3+4 m &=15-2 m \\
3+4(2) & \stackrel{?}{=} 15-2(2) \\
3+8 & \stackrel{?}{=} 15-4 \\
11 &=11 \quad \text { Yes! }
\end{aligned}\)