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 then 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.

How to solve an equation with variable on both sides

Before you could begin to solve questions on equation or variable I want you to note the simple definition below.

What are variables?

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

I would say variable means alphabet used to represent an unknown value in a lame man description. Hope that’s easy to understand right? Let’s push on towards the equation.

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What is an equation?

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

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

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

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 know 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 that if a variable and equation appear in a question.

  • First of all, check whether the variable occurs twice: Whenever a variable appears twice in a given question together with a sign what you should do is either put them together by subtracting them or adding them based on the sign present 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 we have 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 are having with it either 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.
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After knowing all listed above let us pick up questions and give justice to them.

This explains it better…

Questions and answers on equation with variable on both side

  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 number or variables that look alike. Don’t forget if a number or variable is crossing the equal to the sign will surely change.
  • Let us move 1 to 13 and 4x to x because the 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 side by the co-efficient 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 step by step
  • -8 = -3x+x
  • Plus comes first
  • -8 = x-3x
  • -8 = -2x
  • Divide both side 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 side by 18
  • n=-1
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Use numbers 4 & 5 as exercise and drop your answers and any question in the comment box below. I won’t give a 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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