Algebra: Solve Linear Equation Practice 1
This section includes 6 focused practice questions to help you reinforce the rules and techniques for solving algebraic linear equations using the balancing equation method.
Related Lessons:
Practice 1 - Question 1
Solve the equation \(x-\left(2x-8\right)=28+4x\)
Solution:
\[
\begin{align*}
x-\left(2x-8\right)&=28+4x\\
x-2x+8&=28+4x\\
-x+8&=28+4x\\
-x-4x&=28-8\\
-5x&=20\\
&=\frac{20}{-5}\\
&=-4\\
\end{align*}
\]
Practice 1 - Question 2
Solve the equation \(\frac{w}{5}+57=-\frac{3}{4}w\)
Solution:
\[
\begin{align*}
\frac{w}{5}+57&=-\frac{3}{4}w\\
\frac{1}{5}w+\frac{3}{4}w&=-57\\
\frac{19}{20}w&=-57\\
w&=\frac{-57}{\left(\frac{19}{20}\right)}\\
&=-60\\
\end{align*}
\]
Practice 1 - Question 3
Solve the equation \(6=16-2x\)
Solution:
\[
\begin{align*}
6&=16-2x\\
2x&=16-6\\
2x&=10\\
x&=\frac{10}{2}\\
m&=5\\
\end{align*}
\]
Practice 1 - Question 4
Solve the equation \(\frac{7}{2a-1}=\frac{2}{a+1}\)
Solution:
\[
\begin{align*}
\frac{7}{2a-1}&=\frac{2}{a+1}\\
7\left(a+1\right)&=2\left(2a-1\right)\\
7a+7&=4a-2\\
7a-4a&=-2-7\\
3a&=-9\\
a&=-3\\
\end{align*}
\]
Practice 1 - Question 5
Solve the equation \(2b-5=4-3\left(b+2\right)\)
Solution:
\[
\begin{align*}
2b-5&=4-3\left(b+2\right)\\
2b-5&=4-3b-6\\
2b-5&=-3b-2\\
2b+3b&=-2+5\\
5b&=3\\
b&=\frac{3}{5}\\
\end{align*}
\]
Practice 1 - Question 6
Step By Step Full Solution
Below is the complete step-by-step solution for the six practice questions above. Mastering algebraic equations goes beyond simply reading the answers — it requires understanding and applying the correct techniques at every step. Students who find algebra challenging are strongly encouraged to go through the video solutions and focus on how each step is developed. With consistent practice, students will discover that once they gain confidence in algebra, their overall Mathematics ability improves significantly.