Two Step Equations II

Parking Diagram
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When we park a car, there are two main steps: backing and turning in, then straightening up.

When we leave the parking bay, we REVERSE these steps by turning out, going forward, and entering back onto the roadway.

Shoes and Socks Pic
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When we get dressed for school we put on our socks and then our shoes.

When we change into our Sports uniform, we reverse this process and take off our shoes and then take of our socks.

We do the Opposites in the Reverse Order.

The same concept applies to equations.

To build an equation, operation steps have been done to a letter variable.

To solve an equation we do the opposite steps in reverse order.

Solving Two Step Equations Using Opposites

Using this concept, We can solve two step equations without drawing Flowcharts.

We still follow the same basic mathematical method, which involves these steps.

1) Work out what operations have been done to the variable letter
2) Put these operations into BODMAS or PEMDAS order
3) Work out what the Opposite Operations are
4) Put the Opposite Operations into SAMDOB or SADMEP order
5) Apply the Opposites one by one to both sides of the equation
6) Simplify the final answer

Here is a summary of the six step process.

Summary of Six Steps

Step 1 – Operations on Variable Letter

The first step involves working out the the operations that are applied to our letter variable.

Let’s do an example of 2N + 5 = 11 as our equation to solve.

1) The operations on N are + 5 and x2.

Step 2 – Put Operations into Order

The “Order of Operations” is called “PEMDAS” in the USA, and “BODMAS” in Australia. Other countries have very similar sets of rules.

BODMAS slide

For our example: 2N + 5 = 11

1) Operations are + 5 and x2
2) BODMAS or PEMDAS for these is x2 then + 5

Step 3 – Determine Opposite Operations

The third step involves working out the “Opposite” operations.

We can do this using the following table.

Back Tracking Opps Slide

For our example: 2N + 5 = 11

1) Operations are + 5 and x2
2) BODMAS or PEMDAS for these is x2 then + 5
3) Opposites are /2 and -5

Step 4 – Opposite Operations in Reverse Order

We take our opposites from the previous step, and put them into reverse BODMAS or PEMDAS order, which means they need to go into SAMDOB or SADMEP order.

For our example: 2N + 5 = 11

1) Operations are + 5 and x2
2) BODMAS or PEMDAS for these is x2 then + 5
3) Opposites are /2 and -5
4) SAMDOB or SADMEP order is -5 then /2

The first four steps we have done can be summarised as follows:

Example A step 1
Step 5 – Apply Opposites to the Equation

In this step we apply each opposite, in SAMDOB or SADMEP order, one by one to both sides of the equation.

On the left side, operations should cancel out, and eventually simplify to give the letter on its own.

For our example: 2N + 5 = 11

1) Operations are + 5 and x2
2) BODMAS or PEMDAS for these is x2 then + 5
3) Opposites are /2 and -5
4) SAMDOB or SADMEP order is -5 then /2

Shown below is the working out we do to complete Step 5.

Example A Step 2
We have applied the Step 4 operations to both sides of the equation, and thereby obtained the solution answer.

Checking Solutions Using Substitution

We can always check the solution to any equation by substituting the number answer we obtained back into the original equation.

Here is how we can check the N=3 solution for the equation 2N + 5 = 11.

Check Solution

Solving Two Step Equations – Examples

Here are some examples for you to try.

Simply complete the missing items on each of the items below.

Ex 1 step 1

Here is how we apply the Step 4 operations to both sides of the equation, and thereby obtain the solution answer.

Ex 1 step 2

Here is an example that involves a fraction variable, which means Division is occurring.

Ex 2 step 1

Here is how we apply the Step 4 operations to both sides of the equation, and thereby obtain the solution answer.

Ex 2 step 2

This final example has Brackets in it, which must be done first, regardless of what operation is inside them.

Ex 3 step 1

Here is how we apply the Step 4 operations to both sides of the equation, and thereby obtain the solution answer.

Ex 3 step 2

Videos About Solving Two Step Equations

Here is a video about solving two step equations.

Here is a video which goes all the way through solving equations, from one step equations to two step equations.

Here is another video that ties one step equations in with two step equations really well.

The following video involves solving two step equations that have positive and negative Integer numbers in them.

This final video shows some challenging Equation questions that involve Fractions.

Presentation on Solving Two Step Equations

Two Step Equation Game

“Equation Millionaire” is a game that will challenge your two step equations solving skills.

Equations Millionaire Game Pic Link

This game has a mixture of difficulties, ranging from single step with negative numbers, through to brackets equations and fractions.

It has a set of three “hints” that are like lifelines, and give clues such as “The answer is not D”.

This game can be played by clicking the following link.

Click here to play Equations Millionaire

Related Items

How to Translate Word Problems into Equations
Solving One Step Addition Equations
Solving One Step Subtraction Equations
Solving One Step Equations – All Types
Two Step Equations Using Flowcharts and Back Tracking
Three Step Equations Using Flowcharts and Back Tracking
Balance Beam Equations
Equivalent Equations
Fractions Equations
Solving Equations Word Problems
eBay Problem Solved Using Algebra Equations
Microsoft Mathematics Equations Solver
Equations Games

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