Solving Linear Equation - Part 1

Lesson Objective

This lesson shows you the basics that you need to know when solving linear equations.

About This Lesson

If you are asked to find the value of x in the equation:
x + 2 = 3

You can immediately solve the equation by letting x = 1. This is because both sides of the equation must be equal to 3 for this equation to remain true.

Now, this lesson shows the basics that you need to know when solving linear equations. These basics are very useful when it comes to solving more complicated equations.

Study Tips

Tip #1

For linear equations, the variable (or unknown) that you need to find has only one value (i.e. one correct answer)

Tip #2

An equation has 2 sides. One is called Left Hand Side (LHS) and another is called Right Hand Side (RHS). For example, consider the equation:

x +2 = 3

The LHS is x+2 and the RHS is 3.

Tip #3

Realize the importance of the equal sign (=) in an equation. This sign means that both sides of the equation must balance up each other.

So, whatever is added in the LHS must be equally be added in the RHS

Tip #4

The math video shows some shortcuts that can be used for solving linear equations quickly. You may want to learn these shortcuts.

Now, watch the following math video on to know more.

Math Video

Click play to watch

If the above player doesn't work, try this direct link.

Math Video Transcript

00:00:00.210
This lesson shows you  the basics behind solving linear equations.

00:00:07.100
Consider the equation x + 5 = 8. To solve this equation, our objective is to find the  value of x. This means what is  x equals to?

00:00:19.230
To do so, logically, we must remove +5.  

00:00:25.060
So, we add  - 5 into the left hand side of the equation. 

00:00:30.140
From here, since we add  -5 to the left hand side. You must also add the  -5 on the right hand side.

00:00:38.240
Why must we do so?. This is because, of the equal sign here. So, Whatever terms you add on the left hand side must be equally balanced by the right hand side. 

00:00:50.240
Now, +5 and  -5 cancels off each other. This leaves us with x = 8 -5.

00:00:59.210
We can now solve this equation by minus 8 with 5. This gives 3.  So the answer is x = 3.

00:01:10.060
Now, After understanding the logic behind, we can use a shortcut to solve this equation. 

00:01:18.010
We can simply just move the +5 to the other side. Remember, when you move it, just have to change the sign to the opposite sign. In this case, we change the sign from positive to negative.

00:01:32.010
Let me show you. See that, the positive sign changes to negative sign when i move it over. Now, why do we need to change the sign?  

00:01:43.030
This is because when we move +5, this is the same as removing +5 by adding with -5. 

00:01:51.070
So, when you put it on the other side, it must become  -5. Observe that this works the same way, if I move -5 back. 

00:02:05.220
Now, minus 8 with 5. This gives 3.

00:02:13.220
Next, let's solve x -2 = 8.  Keeping the objective in mind, we need to remove -2, to remove -2, we add  +2 to the left hand side

00:02:29.110
Since we add +2 to the left hand side, we need to balance up by adding  +2 to the right hand side. 

00:02:37.230
Now,  -2 and +2 cancels off each other.  We solve this equation by adding 8 with 2. This gives 10.

00:02:47.110
Now, we have x = 10. 

00:02:51.090
We can use the shortcut to solve for x. To do so, we can simply move -2 to the other side. 

00:03:00.160
Again, we must change the sign. So,the negative sign becomes a positive sign. If I bring it back, becomes to -2.

00:03:16.060
Again, why do we need to change the sign?  This is because, when we move -2, we are actually removing -2 by adding it with  +2.

00:03:28.160
So, when you put it on the other side, it becomes  +2. This is the same idea as the previous example.

00:03:37.230
Now add 8 with +2 . We  get 10. 

00:03:43.230
Next example, solve 3x = 9.  Keeping the objective in mind, we know that we need to remove 3. 

00:03:54.050
To do so, logically, we divide 3x by 3.  Similarly, to keep the equation balanced, we also must divide 9 by 3.

00:04:06.170
Now, 3 divides by 3 cancels off each other. We are left with x =9/3. 9 divides by 3 gives 3. 

00:04:19.140
So, the answer is x = 3. Let's use the shortcut to solve this equation.

00:04:28.030
Since 3 is actually multiplied by x, when we move 3 to the other side, it becomes divide. Notice there is no change in sign. Let me explain why.

00:04:41.020
This is because, when we divide by both sides by 3. there are no manipulation in sign. Therefore, we do not need to change the sign.

00:04:51.200
To solve this equation, we divide 9 with  3. So, the answer is x equals to 3. 

00:05:02.000
Next, let's solve x/7 = 2. To find x, we need to multiply left hand side by 7. To balance up, we also must multiply right hand side by 7.

00:05:16.240
Now, 7 and 7 cancels off each other. Hence, we get x = 7 bracket two. 7 multiply by 2 gives 14.

00:05:29.210
As for the shortcut. Since 7 is used to divide x, when we bring it up, its operation becomes multiply. Note that you must put brackets around all the terms in this side. 

00:05:44.100
Notice there is no change in sign. The reason for this is similar to the previous example. 

00:05:51.080
Now multiply 7 x 2. You will get x =14. 

00:05:56.210
That is all for this lesson. Part 2 will have more explanations and examples on how to solve linear equations using what you have learned so far.

Practice Questions & More

Multiple Choice Questions (MCQ)

Now, let's try some MCQ questions to understand this lesson better.

You can start by going through the series of questions on solving linear equation or pick your choice of question below.

Question 1 on the basics of solving linear equation
Question 2 on the basics of solving linear equation

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