Equations
New Zealand
Level 6 - NCEA Level 1
Solve Equations with rational expressions
Lesson
We've already looked at how to solve equations, whether that be in one, two or three steps. As you know, equations can involve a number of different operations and there are different methods for solving equations so click here if you need a refresher.
In this chapter, we are going to look at examples of equations that involve addition and subtraction of algebraic terms, including ones with fractions.
Examples
Question 1
Solve $\frac{-7}{100}+\frac{x}{100}=\frac{7x}{100}+\frac{7}{100}$−7100+x100=7x100+7100 for $x$x.
Think: How do we move these terms around to get $x$x by itself.
Do:
| $\frac{-7}{100}+\frac{x}{100}$−7100+x100 | $=$= | $\frac{7x}{100}+\frac{7}{100}$7x100+7100 | Multiply all the terms by the common denominator, $100$100 |
| $-7+x$−7+x | $=$= | $7x+7$7x+7 | Rearrange the expression so all the $x$x terms are on one side |
| $-7-7$−7−7 | $=$= | $7x-x$7x−x | Now let's simplify |
| $-14$−14 | $=$= | $6x$6x | |
| $\frac{-14}{6}$−146 | $=$= | $x$x | Make $x$x the subject and simplify the fraction |
| $x$x | $=$= | $\frac{-7}{3}$−73 |
Question 2
Solve the following equation: $5x-\frac{104}{5}=x$5x−1045=x
Question 3
Solve the following equation: $\frac{5x}{3}-3=\frac{3x}{8}$5x3−3=3x8