We've learnt a lot about solving equations including how to solve one step, two step and three step equations, as well as equations that include fractions. We've also looked at how to group variables (ie. algebraic letters) when they are written on both sides of equation.
In a nutshell, we backtrack using a reversed order of operations and make the variable the subject of the equation.
We need to keep our equations balanced.
Whatever you do to one side, you have to do to the other.
Examples
Question 1
Solve: $\frac{3x}{5}-4=-16$3x5−4=−16
Think: How do we get $x$x by itself?
Sometimes the way to work this out is to write down what is happening to the $x$x - by order of operations.
In this case we have $x$x
- is being multiplied by $3$3
- then divided by $5$5
- then $4$4 is subtracted from that
So to reverse this order, will give us the $x$x on its own.
Do:
| $\frac{3x}{5}-4$3x5−4 | $=$= | $-16$−16 | Add $4$4 to both sides |
| $\frac{3x}{5}$3x5 | $=$= | $-12$−12 | Multiply both sides by $5$5 |
| $3x$3x | $=$= | $-60$−60 | Divide both sides by $3$3 |
| $x$x | $=$= | $-20$−20 |
Question 2
Question 3
Solve for the unknown.
$\frac{1}{x}-\frac{10x}{3}=-\frac{7}{3}$1x−10x3=−73
Write all solutions on the same line, separated by commas.