Equations

NZ Level 7 (NZC) Level 2 (NCEA)

Solve Equations with Rational Expressions

Lesson

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 pronumerals (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 pronumeral the subject of the equation.

Remember!

We need to keep our equations balanced.

Whatever you do to one side, you have to do to the other.

Solve: $\frac{3x}{5}-4=-16$3`x`5−4=−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 |

Solve for the unknown.

$\frac{1}{x}-\frac{10x}{3}=-\frac{7}{3}$1`x`−10`x`3=−73

Write all solutions on the same line, separated by commas.

Form and use linear, quadratic, and simple trigonometric equations

Apply graphical methods in solving problems

Apply algebraic methods in solving problems