Solving Linear Equations - Part 1
This lesson shows you the basics behind 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.
For linear equations, the variable (or unknown) that you need to find has only one value (i.e. one correct answer)
An equation has two sides. One is called Left Hand Side (LHS) and the other side is called Right Hand Side (RHS). For example, consider the equation:
x + 2 = 3
The LHS is x+2 and the RHS is 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 to the LHS must be also added to the RHS.
The math video shows some shortcuts that can be used for solving linear equations. You may want to learn these shortcuts.
Now, watch the following math video to know more.
Click play to watch
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Math Video Transcript
This lesson shows you the basics behind solving linear equation.
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?
To do so, logically, we must remove +5.
So, we add - 5 into the left hand side of the equation.
From here, since we add -5 to the left hand side. You must also add the -5 on the right hand side.
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.
Now, +5 and -5 cancels off each other. This leaves us with x = 8 -5.
We can now solve this equation by minus 8 with 5. This gives 3. So the answer is x = 3.
Now, After understanding the logic behind, we can use a shortcut to solve this equation.
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.
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?
This is because when we move +5, this is the same as removing +5 by adding with -5.
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.
Now, minus 8 with 5. This gives 3.
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
Since we add +2 to the left hand side, we need to balance up by adding +2 to the right hand side.
Now, -2 and +2 cancels off each other. We solve this equation by adding 8 with 2. This gives 10.
Now, we have x = 10.
We can use the shortcut to solve for x. To do so, we can simply move -2 to the other side.
Again, we must change the sign. So,the negative sign becomes a positive sign. If I bring it back, becomes to -2.
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.
So, when you put it on the other side, it becomes +2. This is the same idea as the previous example.
Now add 8 with +2 . We get 10.
Next example in solving linear equation, solve 3x = 9. Keeping the objective in mind, we know that we need to remove 3.
To do so, logically, we divide 3x by 3. Similarly, to keep the equation balanced, we also must divide 9 by 3.
Now, 3 divides by 3 cancels off each other. We are left with x =9/3. 9 divides by 3 gives 3.
So, the answer is x = 3. Let's use the shortcut to solve this equation.
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.
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.
To solve this equation, we divide 9 with 3. So, the answer is x equals to 3.
Next example in solving linear equation. 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.
Now, 7 and 7 cancels off each other. Hence, we get x = 7 bracket two. 7 multiply by 2 gives 14.
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.
Notice there is no change in sign. The reason for this is similar to the previous example.
Now multiply 7 x 2. You will get x =14.
That is all for this lesson in solving linear equation. 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 equations or pick your choice of question below.
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