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:
\[
\begin{align*}
2b-5&=4-3\left(b+2\right)\\
2b-5&=4-3b-6\\
2b-5&=-3b-2\\
2b+3b&=-2+5\\
5b&=3\\
b&=\frac{3}{5}\\
\end{align*}
\]