Algebra: Solve Linear Equation - 7 Examples
Now that you have learned how the balancing equation technique works, let’s go through 7 examples together to strengthen your understanding and build your confidence in applying the method.
Related Lessons:
Example 1 of 7
Solve the equation \(2\ +\ 7x\ =\ -70+16x\)
Solution:
Solution:
\[
\begin{align*}
2+7x&=-70+16x\\
7x-16x&=-70-2\\
-9x&=-72\\
x&=frac{-72}{-9}\\
x&=8\\
\end{align*}
\]
Example 2 of 7
Solve the equation \(0.38x+3.5=0.18x-1.3\)
Solution:
Solution:
\[
\begin{align*}
0.38x+3.5&=0.18x-1.3\\
0.38x-0.18x&=-1.3-3.5\\
0.2x&=-4.8\\
x&=\frac{-4.8}{0.2}\\
x&=-24\\
\end{align*}
\]
Example 3 of 7
Solve the equation \(9x\ +\ 17\ =\ 7(3\ +\ x)\)
Solution:
\[
\begin{align*}
9x+17&=7\left(3+x\right)\\
9x+17&=21+7x\\
9x-7x&=21-17\\
2x&=4\\
x&=\frac{4}{2}\\
x&=2\\
\end{align*}
\]
Example 4 of 7
Solve the equation \(\left(x-10\right)+11\left(x-3\right)=3x+5\)
Solution:
\[
\begin{align*}
\left(x-10\right)+11\left(x-3\right)&=3x+5\\
x-10+11x-33&=3x+5\\
12x-43&=3x+5\\
12x-3x&=5+43\\
9x&=48\\
x&=\frac{48}{9}\\
x&=5\frac{1}{3}\\
\end{align*}
\]
Example 5 of 7
Solve the equation \(5(x+3)-2(x-2)=7\)
Solution:
\[
\begin{align*}
5\left(x+3\right)-2\left(x-2\right)&=7\\
5x+15-2x+4&=7\\
3x+19&=7\\
3x&=7-19\\
3x&=-12\\
x&=\frac{-12}{3}\\
x&=-4\\
\end{align*}
\]
Example 6 of 7
Example 7 of 7
Solve the equation \(\frac{x-4}{3}-4=\frac{7x}{2}\)
Solution:
\[
\begin{align*}
\frac{x-4}{3}-4&=\frac{7x}{2}\ \ \ \ \ \ \times6\\
2\left(x-4\right)-24&=21x\\
2x-8-24&=21x\\
2x-32&=21x\\
2x-21x&=32\\
-19x&=32\\
x&=\frac{-32}{19}\\
x&=-1\frac{13}{19}
\end{align*}
\]