# Two Step Equations

Lesson

We have already seen how to solve Single Step Equations. These ones seemed almost too simple to use a series of rules or steps to solve. Time to take it to the next level.

## Two Step Equations

A two step equation is one that will require two steps to solve. They generally have a multiplication/division and a subtraction/addition. The following are all two step equations.

$2x+5=11$2x+5=11,          $\frac{1}{3}h-3=6$13h3=6,         $19-2j=5$192j=5

Let's look at two methods for solving two step equations.

### Method 1 - Backtracking

Two step equations can be set up using a backtracking tool.

Start by writing the pronumeral (variable) in a box. Then one step at a time mark in the operations that happen in order (according to Order of Operations). Remember we learnt how to set up equations in backtracking here.

#### Example

Solve: $-2x+4=8$2x+4=8

Think: First we need to set up the equation.

 × $-2$−2 $+$+$4$4 $x$x $8$8

Do: Backtrack one step at a time, reversing each operation.

 × $-2$−2 $+$+$4$4 $x$x $4$4 $8$8
 × $-2$−2 $+$+$4$4 $-2$−2 $4$4 $8$8

So $x=-2$x=2.

With all equations we can check our solution. Does $x=-2$x=2 satisfy the equation $-2x+4=8$2x+4=8?

### Method 2 - Use formal algebraic techniques

This means using the "do the same to both sides" method, to isolate the $x$x. That is, get the $x$x on its own.

It is all about reversing the operations. So, we will need to remove the constant (number) term first. This is done by choosing the reverse operation.

$-2x+4=8$2x+4=8

 $-2x+4$−2x+4 $=$= $8$8 The opposite of addition is subtraction. $-2x+4-4$−2x+4−4 $=$= $8-4$8−4 Start by subtracting $4$4 from both sides. $-2x$−2x $=$= $4$4 Simplify both sides of the equation $\frac{-2x}{-2}$−2x−2​ $=$= $\frac{4}{-2}$4−2​ Then identify the next operation that needs to be reversed. The opposite of multiplying by $-2$−2 is dividing by $-2$−2. $x$x $=$= $-2$−2 Simplify both sides to find $x$x

#### Worked Examples

##### Question 1

Solve the following equation:

$8m+9=65$8m+9=65

##### Question 2

Find the solution for the following equation: $\frac{x+9}{7}=4$x+97=4

##### Question 3

Solve the following equation: $5\left(y+1\right)=25$5(y+1)=25

### Outcomes

#### NA4-7

Form and solve simple linear equations