Equations

NZ Level 4

Introduction to Equations

Lesson

An equation is a statement that says that two things are the same, or equal.

An equation will always contain an equals sign or "="

$3x+2=4$3`x`+2=4

Equations normally contain letters that stand for unknown numbers. These letters are called variables or pronumerals. In the example above, the variable is $x$`x`. Any letter can be used as a variable. There can be more than one variable in an equation, and variables can appear on either side of the equals sign.

$20a=40$20`a`=40

$5=14-3f$5=14−3`f`

$\frac{5c}{7}=g+2$5`c`7=`g`+2

An equation is like a sentence. You can translate any wordy maths problem into an equation.

The most important thing about an equation is that it must have an equals sign and that the value of both sides of the equal sign must be the same. They don't have to look the same, just have the same value.

Adam thought of a number, doubled it and added $5$5 to get $13$13. What number did he start with?

Can be translated into the equation:

$2x+5=13$2`x`+5=13

Similarly:

Three apples cost a dollar more than two bananas.

Can be represented using the equation:

$3a=2b+1$3`a`=2`b`+1

Using any of the four operations (addition, subtraction, multiplication and division), write an expression for '15 less than a'.

Write an algebraic expression for '15 times the result of v reduced by 6'.

Write an algebraic expression for '$15$15 less than the quotient of $p$`p` and $6$6'.

Form and solve simple linear equations