2.01 Linear equations
The aim of solving a linear equation is to work out the unknown value, such as $x$x. To solve for the unknown, we want to transpose the equation so that $x$x is the subject of the equation. To do this, we apply inverse (opposite) operations to both sides.
The most important thing to remember is that both sides of the equation must remain balanced. Always remember; any operation applied to one side of an equation must be applied identically to the other side of the equation.
To double check if an answer is correct, we can substitute the answer back into the original equation. If the two sides of the equation are equal, then the answer found must be correct.
Practice questions
question 1
Solve the following equation: $8m+9=65$8m+9=65
Question 2
Find the solution for the following equation: $\frac{x+9}{7}=4$x+97=4
Question 3
Solve the following equation:
$3x-8=x$3x−8=x
Question 4
Solve: $4\left(5x+1\right)=-3\left(5x-5\right)$4(5x+1)=−3(5x−5)
Question 5
The number of years, $y$y, a person born in Japan is expected to live can be approximated by the equation $y=0.27x+72$y=0.27x+72, where $x$x is the number of years since 1970.
Solve this equation for $x$x.
Hence determine $x$x, the number of years after 1970 the approximate life expectancy will be $86$86. Give your answer correct to 3 decimal places where appropriate.
Hence, in which year will the approximate life expectancy in Japan be $86$86 years?
$2022$2022
A$2056$2056
B$2021$2021
C
Solving linear equations using technology
Linear equations can also be solved using technology, such as a graphics calculator. The video below explains how to use a graphics calculator to quickly produce a solution to any given linear equation.
[Calculator instructions coming soon]
Practice questions
Question 6
Solve the following linear equation using technology.
$6x+10=4x+18$6x+10=4x+18
Question 7
Solve the following linear equation using technology.
$\frac{5x-15}{4}=-20$5x−154=−20