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CanadaON
Grade 12

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$77 $=$= $7x-x$7xx 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$5x1045=x

Question 3

Solve the following equation: $\frac{5x}{3}-3=\frac{3x}{8}$5x33=3x8

 

 

Outcomes

12F.C.3.6

Solve simple rational equations in one variable algebraically, and verify solutions using technology

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