One Step Equations

The one step equations worksheets on this page include problems with integers and fractions for a variety of math operations. These basic algebra worksheets are appropriate practice for 6th grade, 7th grade and 8th grade students. Full answer keys are included on the second page of each PDF file.

Working with One Step Equations

These one step equations worksheets will teach you the proficient ways on how to do one step equations, covering some of the most useful skills in mathematics in order for your critical thinking skills to be enhanced! To do this, practice with some easy algebra equations to get you in the rhythm of things. But first, let us start with the definition of one step equations.

What Are One Step Equations?

Let us start by first defining what an equation is, the answer to that is simple: an equation is a statement that shows two expressions who are equal to each other. This mathematical sentence, when referring to its other elements, brings up the topic of one-step equations – one of the most basic and essential algebraic skills needed for solving math problems, and will be this article’s subject matter! Within 1 step equations are the following fields: addition, subtraction, multiplication, and division. With this, we will also be focusing on some of its subcategories such as: solving with positive and negative integers, fractions, and decimals. Now, let’s get to work with some examples!

With the meaning in its name– one step equations only require one step to solve. To prove that, check out some of the examples from one of the worksheets to express such.

Solving One Step Equations

Positive and Negative Integers Equations

Starting with the basics, let’s define what positive and negative integers are and how they affect the process of solving for equations. This topic could be difficult for some learners, but stating some of the facts about this case might help you get the gears in your brain turning. “How to do a one step equation,” you ask? Continue reading to figure out how!

“0” is neither a positive integer, nor is it a negative one. And with that, we can conclude that anything after “0” is a positive number; anything below it, immediately negative. Here are some easy algebra equations below. A step-by-step guide will be provided, followed by a detailed discussion on each step.

Example 1: Integers Addition

4 + x = 5

Step 1: Isolate “x” by putting “4” to the other side of the mathematical sentence. When moving a positive number to the opposite part of the equation, positive should turn into negative; “4” to “-4”. This leaves us with the equation shown below. This is an example of an equation with a negative integer.

x = 5 - 4

Step 2: Solve for the subtraction question “5 - 4”, this will lead to the answer which is “x = 1”.

x = 1

Example 2: Integers Subtraction

4 - x = 5

Step 1: On your paper, write down the equation that is shown above. This will help you visualize the numbers more clearly; therefore, making it easier for you to calculate. Place the “4” on the right hand side in order to isolate the “x”.

-x = 5 - 4

Step 2: Do the necessary calculations. In this case it is “5 - 4”, with that you will get “1”.

-x = 1

Step 3: A rule that we should remember is that the “x” should never be negative, but with this specific number, “x” is with a negative sign. To change this, put the “-” negative sign onto the other side, to the “1”. To conclude, the answer is “-1”.

x = -1

Example 3: Integers Multiplication

4x = 5

Step 1: Start by simplifying the equation by moving the “4” to the other side. But instead of it being “• 4” (times 4), like moving positive integers, we should switch times into divide, like so: “x = 5 ÷ 4”.

x = 5 ÷ 4

Step 2: Answer “5 ÷ 4”, and with that, you will get “x”, 5/4 or 1.25 in decimal form.

x = 5/4 or 1.25

Example 4: Integers Division

x/4= 5

Step 1: Just like solving for a multiplication equation, we need to do the reciprocal of that number, in this problem, “4” is in question for that. Change the sign to its opposite; divide “÷” to times “*”.

x = 5 * 4

Step 2: And now, solve. You are left with “20” as the answer.

x = 20

One Step Equations With Decimals

With decimals, this can be a little bit more tricky than the previous questions that we have tackled, but fear not as with just enough practice, you will be able to master the art of solving these kinds of problems.

Same (from the positive and negative integers) rules apply!

If any of the steps confuse you, scan through the process that we went through for the positive and negative integers category as a guide.

Example 1: Decimals Addition

2.5 + x = 6.5

x = 6.5 - 2.5

x = 4

Example 2: Decimals Subtraction

2.5 - x = 6.5

-x = 6.5 - 2.5

-x = 4

x = -4

Example 3: Decimals Multiplication

2.5x = 6.5

x = 6.5 ÷ 2.5

x = 2.6

Example 4: Decimals Division

x/2.5 = 6.5

x = 6.5 * 2.5

x = 16.25

One Step Equations With Fractions

Now onto fractions! The process of solving for fractions is the same as decimals as both represent the same number, just in different forms. Just as tricky as decimals, so if you have mastered that, solving these kinds of questions on the one step worksheets will be a piece of cake!

Same (from the rest that were mentioned before) rules apply!

Again, if any of the steps confuse you, scan through the process that we went through for the positive and negative integers category as a guide.

Example 1: Fractions Addition

x = 3/5 - 9/2

x = -39/10

Example 2: Fractions Subtraction

9/2 - x = 3/5

-x = 3/5 - 9/2

-x = -39/10

x = 39/10

Remember that since we need to put the “-” sign to the other side, that negative will cancel out that sign. Or another way to understand it is that the negative from the left hand side will be transferred, keep this rule in mind: “-” + “-”= “+”.

Example 3: Fractions Multiplication and Division

9x/2 = 3/5

9x = 3/5 * 2

9x = 6/5

x = 6/5 ÷ 9

x = 2/15

One Step Equation Examples

Here are some examples from the solving equations worksheets that we will dive into! Delve into it deeper with explanations, like how we did in the other sections. This time, we will be tackling some of the questions that are deemed difficult, but fret not as with a little training, you will be able to solve them easily in no time! Check these sample questions from our one step equations worksheet pdf (solve for x worksheets) out:

Let us start with the simple ones first. As we know, isolating the “x” on one side is the easiest way to get the answer. By doing that, you get the problem laid out for you to solve, just like that.

Example 1:

x + 1 = 5

x = 5 - 1

x = 4

Solve “5 - 1”, and you’ll get the answer. This is an example of an integers equation!

Example 2:

2x = 4

A multiplication question this time, still fairly simple. When moving the “2”, remember that if it is in a times or divide sense, we must switch its sign. In context of this number, since we will be shifting “2” onto the other side, instead of “*2” (times 2), change it to “/2” (divide into 2).

x = 4/2

“4” divided by “2”, you get “2” which is the correct answer.

x = 2

Example 3:

x - 3/5 = -8/5

Move 3/5, not forgetting about changing its sign from negative to positive.

x = -8/5 + 3/5

Add the two together, being cautious of the “-8/5” when calculating the right answer for solving one-step equations.

x = -5/5

Simplify that, “-1” is your answer.

x = -1

Example 4:

13x/39 = 21

Simply take the fraction away from the variable “x” and place the denominator “39” to the other side where it can be multiplied by “21”. Remember, change its form when moving to a different sign, do not make the rookie mistake!

13x = 21 * 39

13x = 819

Divide both sides by 13.

13x ÷ 13 = 819 ÷ 13

Simplify the fraction and you will find the answer that you are looking for. The correct answer is “x = 63”.

x = 63

Example 5:

x + 2 = 5.5

Like we’ve done for the other numbers, go ahead and place that positive “2” over to the right hand side. And do not forget to change its sign, that is very crucial and you should not miss it!

x = 5.5 - 2

Do the calculations and there you have it, you get your answer! In this case, it is “x = 3. 50”.

x = 3. 50

There you have it! You are now ready to practice more by checking out our equations worksheets. We have created different kinds - from simple equations worksheets, solve for x worksheets, to more complicated ones. But worry not! All of our worksheets have answer keys with solutions (not just the final answer). You can always check on your work and understand how each problem was solved. Good luck!