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One-step equations – The simplest type of equations

one-step equations

In this lesson we are going to talk about one-step equations. An equation consists of two equally valuable expressions. An equation can be written in the form of N = M, where N and M are expressions and at least one of them contains at least one variable. There are different types of equations, but we will focus on algebraic one-step equations in this lesson.

One-step equations are equations that can be solved in a single step. That means that we only need to perform a single mathematical operation in order to solve the equation. As a result, we are going to find the value of the variable (named x in our case).
An example of a one-step equation that includes addition is:

one step equations example

This equation consists of the variable x and two constants, the numbers 2 and 5. The variable x is the unknown number whose value we need to find.
To find out the value of the unknown number in the example above, we need to get rid of the 2 on the left side of the equation. We need to get the equation in form of \ x = expression.

When we calculate the expression, we will get a number and that will be the value of our variable x. In our example, we will do that by subtracting the number 2 from both sides of the equation. It should look like this:

solving the one-step equation

The value of our variable is 3.

Here is another example of a one step equation, but this one includes subtraction:

one-step equation subtraction

We can see that we have – 5 as a constant on the left side. We need to get rid of that number to get the equation into the form “x equals a number”. In order to achieve that, we simply add 5 to both sides of the equation.

solving one-step equations subtraction

The result is \ x = 6.

The one-step equations can also contain multiplication or division. A one-step equation with multiplication can be solved by dividing both sides of the equation with the coefficient, which is the number that is multiplied by x.

one-step equations with coefficient

This example has been solved by dividing both sides of the equation with 6, since we need to get rid of the 6 on the left side of the equation.

solving one-step equations with coefficient

The result is \ x = 3.

A one-step equation that includes division can be solved in similar way. We just need to multiply both sides of the equation with the number that divides x.

one-step equation division

In the example above, we need to multiply both sides by 4.

solving one-step equation division

When we solve the equation, we see that the value of the variable is 20. That means that 20 divided by 4 is 5.

So, this is basically it for the one-step equations. If you want to practice a bit, feel free to use the worksheets posted below. Otherwise, you can follow the link to the other lessons, such as the one on two-step equations.

One-step equations worksheets

  Addition and subtraction of integers (264.1 KiB, 471 hits)

  Addition and subtraction of decimal numbers (276.3 KiB, 354 hits)

  Addition and subtraction of fractions (452.6 KiB, 340 hits)

  Multiplication and division of integers (263.7 KiB, 425 hits)

  Multiplication and division of decimal numbers (279.9 KiB, 344 hits)

  Multiplication and division of fractions (382.4 KiB, 356 hits)

Word problems

  Using addition and subtraction in solving word problems (370.4 KiB, 679 hits)

  Using multiplication and division in solving word problems (284.9 KiB, 619 hits)

  Solve the word problems using basic math operations (347.3 KiB, 259 hits)

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