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Form of two-step equations with examples and worksheets

two-step equations

Most equations require more than one step to find the solution. In this lesson we are going to cover two-step equations. Two-step equations are equations that can be solved in two steps. These equations can be written in form of:

written form of two step equations

where x is the unknown variable, a is the coefficient and b and c are numbers. The coefficient can not be 0 or 1.

When solving this type of equation we should follow this order of operations:
1. addition and subtraction
2. multiplication
3. division

Note that we don’t have to follow this order, but it makes the calculation a lot easier.

Let’s get started with some examples, one of each type of the two-step equation.

two-step equations example

This example can be solved in following steps:
● As we already said, it is a lot easier if we follow the order of operations described above. That means that we should subtract 5 from both sides first.

step one in solving two-step equation

● The result of the previous step is a one-step equation. Now we only need to divide both sides with 2 to get the result for x.

step two in solving two-step equation

● The result is \ x = 1.
Note that in this example we could have done division first and then subtraction, but it would make the solving of the equation more difficult since we would have to deal with fractions and it is easier to deal with regular numbers.

subtraction in two-step equation

The example above can be solved in steps similar to the previous example:
● First we need to add 8 to both sides. The resulting equation is:

step one in solving subtraction of two-step equations

●In this step we only need to divide both sides with 4.

step two in solving subtraction of two-step equations

The result is \ x = 6.

Look at this example that you need to divide to get the solution x:

division of two-step equations

step one in division of two-step equations

● In this step we are going to multiply the equation by 3 and get the result.

step two in division of two-step equations

The result is x=15.

In this example, the x:3 could also be written as a fraction like \frac{x}{3} but the process of solving the equation would be the same. So, if we get an equation that is written in form of the \frac{x}{a} + b = c process of solving would be the same as in the example given above because is the same as x : a.

Two-step equations worksheets

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  Solving word problems using integers and decimals (295.3 KiB, 1,446 hits)

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