Algebra: Solve Linear Equation Practice 2
In this section, you will work through 6 carefully selected questions. Each question is designed to help you apply and master the balancing equation method when solving algebraic linear equations. Focus on showing clear working and applying the technique accurately at every step.
Related Lessons:
Practice 2 - Question 1
Solve the equation \(3x+7\left(x+2\right)=4\left(5-3x\right)+7\)
Solution:
\[
\begin{align*}
3x+7\left(x+2\right)&=4\left(5-3x\right)+7\\
3x+7x+14&=20-12x+7\\
10x+14&=27-12x\\
10x+12x&=27-14\\
22x&=13\\
x&=\frac{13}{22}\\
\end{align*}
\]
Practice 2 - Question 2
Solve the equation \(\frac{b}{2}+\frac{b+5}{3}=2\)
Solution:
\[
\begin{align*}
\frac{b}{2}+\frac{b+5}{3}&=2\ \ \ \ \ \ \ \ \ \ \ \ \ \times6\\
3b+2\left(b+5\right)&=12\\
3b+2b+10&=12\\
5b+10&=12\\
5b&=12-10\\
b&=\frac{2}{5}\\
\end{align*}
\]
Practice 2 - Question 3
Solve the equation \(3\left(x+5\right)=8x-7\)
Solution:
\[
\begin{align*}
3\left(x+5\right)&=8x-7\\
3x+15&=8x-7\\
3x-8x&=-7-15\\
-5x&=-22\\
x&=\frac{-22}{-5}\\
x&=4\frac{2}{5}\\
\end{align*}
\]
Practice 2 - Question 4
Solve the equation \(\frac{2x-1}{5}=\frac{x+3}{8}\)
Solution:
\[
\begin{align*}
\frac{2x-1}{5}&=\frac{x+3}{8}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \times40\\
\left(2x-1\right)&=5\left(x+3\right)\\
16x-8&=5x+15\\
16x-5x&=15+8\\
11x&=23\\
x&=\frac{23}{11}\\
x&=2\frac{1}{11}\\
\end{align*}
\]
Practice 2 - Question 5
Solve the equation \(8a-4=5a+20\)
Solution:
\[
\begin{align*}
8a-4&=5a+20\\
8a-5a&=20+4\\
3a&=24\\
a&=\frac{24}{3}\\
a&=8\\
\end{align*}
\]
Practice 2 - Question 6
Step By Step Full Solution
The following video contains detailed solutions to the six practice questions above, presented in a clear and structured format to guide your learning.
Success in solving algebraic equations is about developing a reliable method and applying it consistently. Each video solution demonstrates the correct technique, explains the reasoning behind every step, and highlights how to avoid common mistakes.
If you find algebra challenging, take time to study the video explanations carefully. Focus on understanding the process rather than rushing to the final answer. Once you build a strong foundation in algebra, you will notice a significant improvement in your overall confidence and performance in Maths.