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How To Solve Equations with Variables on Both Sides

We shall discuss how to solve equations with variables on both sides here. Do you have a little understanding of algebra or not?

If you have, you should find this lecture simple for those who have no idea; smile, because today you will know all about algebra.

Before I go deep into the topic, I’d like to give you a simple indication of how you can address any algebra question. Please bring out a note and a pen to jot things down.

Before you could begin to solve questions on equations or variables, I want you to note the simple definition below.

What are variables?

I have found this so-called variable in various places I’d like to throw light at. I learned a variable was a container holding or storing different values when I learned a programming language called PHP. I’m not going to explain that further because we’re not here for that.

Variable means the alphabet used to represent an unknown value in a lame man description. I hope that’s easy to understand, right? Let’s push on toward the equation.

What is an equation?

I’m going to give that a simple definition too. You may do additional research on the term through google or your dictionary.

The equation is derived from the equal sign, and whenever you see the same in a question, you know it’s an equation.

Not only that, the equation deals with assigning variables. Whenever you say x=5, don’t forget that your x is still identical to 5.

How To Form A Quadratic Equation Whose Roots Are Given

That is how I could explain mine. If you know any other simplest method, drop it in the comment box.

Now that you’ve to know variables and equations, it’s high to understand how to solve equations with variables on both sides.

How to solve questions involving variables and equations

Have this at the back of your mind if a variable and equation appear in a question.

  • First, check whether the variable occurs twice: Whenever a variable appears twice in a given question with a sign, you should put them together by subtracting them or adding them based on the sign in the question. For instance, if you have 5x + 2x = 10. We all know the variable to be x, right? Now check the question very well; you will see two numbers carrying the same variable on the left-hand side. In this case, you will have to add them together. Adding them together gives you 7x. Take heed.
  • Know that the symbol in front of it will change from + to-and vice versa whenever a value or number crosses the equal sign.
  • If a bracket is present in the question, expand the bracket by multiplying it with whatever you have with it, either a sign or number. You are given questions like 6(x+2), for example. You will have to expand the bracket by multiplying it by 6. Your answer will now be 6x+2.
  • If a number variable is equal to a number, e.g., 2x=10. You will have to divide both sides with the coefficient of x, which is 2.

After knowing all listed above, let us pick up questions and give justice to them.

Apon vs. Upon: Master the Usage in English Grammar
YouTube video
This explains it better…

Questions and answers on equations with variables on both sides

  1. 13-4x = 1-x
  2. -8-x = x -4x
  3. -8n+4(1+5n) = -6n-14
  4. n+2 = -14-n
  5. 6r+7 =13+7r


  • 13-4x = 1-x
  • (C.L.T) Collect like terms first, i.e., numbers or variables that look alike. Don’t forget if a number or variable crosses, the equal to the sign will surely change.
  • Let us move 1 to 13 and 4x to x because they are the same
  • 13 – 1 = what we have left on this side, which is (-x). Then (-4x) coming there will be +4x.
  • 13 – 1 = -x + 4x
  • 12 = 4x – x
  • 12=3x
  • Divide both sides by the coefficient of x, which is 3
  • 12/3 = 3x/3
  • x=4
  • -8-x = x-4x
  • Collect like terms
  • -8 = x-4x+x
  • Let’s take it to step by step
  • -8 = -3x+x
  • Plus comes first
  • -8 = x-3x
  • -8 = -2x
  • Divide both sides by -2
  • -8/-2 = -2x/-2
  • x=4
  • -8n+4(1+5n) = -6n-14
  • Expand the bracket by multiplying
  • -8n+4×1+4x5n = -6n-14
  • -8n+4+20n = -6n-14
  • Collect like terms
  • -8n+20n+6n = -14-4
  • Plus comes first
  • 20n+6n-8n = -18
  • 26n-8n = -18
  • 18n = -18
  • Divide both sides by 18
  • n=-1

Also Read:

Use numbers 4 & 5 as an exercise, and drop your answers and any question in the comment box below. I won’t reply to any question not related to the above topic.

If you still don’t understand how to solve equations with variables on both sides, check my profile below and contact me.

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