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:
\[
\begin{align*}
\frac{x-4}{3}-4&=\frac{7x}{2}\ \ \ \ \ \ \times6\\
2\left(x-4\right)-24&=21x\\
2x-8-24&=21x\\
2x-32&=21x\\
2x-21x&=32\\
-19x&=32\\
x&=\frac{-32}{19}\\
x&=-1\frac{13}{19}
\end{align*}
\]
Step By Step Full Solution
Solving algebraic equations is a fundamental skill that every student must master. A weak foundation in basic algebra often leads to difficulties when tackling more advanced algebraic concepts in the future.
The video below provides a clear, step-by-step explanation of the seven examples above, guiding students through the techniques and reasoning behind each step. Students who are weak in Mathematics are strongly encouraged to study the examples carefully and pay close attention to the techniques demonstrated, as consistent practice and understanding are key to improvement.