Linear Equations

Video 1

Video 2

Linear equations are an important part of maths. Lets go through the example in Video 1 to find x.

Question 1:
What does x equal in the linear equation 2x + 3 = 7?
First of all, lets establish that in a linear equation there are two sides, side 1 in our case is equal to 2x + 3 and side 2 is equal to 7. We need to find x which represents a number which would keep both sides balanced.
Instead of the equals sign, visualise a weighing scale with two sides, in our case we have 2x + 3 and 7. To keep the weighing scale balanced as it is now, whatever we do to one side we must do to the other. This ensures that it remains balanced.
We need to find x =
2x + 3 = 7
(Subtract 3 from both sides)
2x + 3 - 3 = 7 - 3
2x = 4
(Divide both sides by 2)
2x/2 = 4/2
x = 2
By subtracting 3 from both sides, we kept the weighing scale balanced, as we treated both sides in the same manner. This left us with
2x = 4
Now think about it, 4 is equal to 2 times an unknown number, to find the value of 1 times an unknown number, we would have divide the value, in this case 4 by 2.
If we did not treat each side equally, then the weighing scale would have not been balanced, each side would not be equal to each other, the fact that it was kept balanced, means the end result of x = 2 would be correct as the two sides are balancing.

AS LONG AS YOU TREAT EACH SIDE EQUALLY YOU CAN TAKE AN ALTERNATIVE APPROACH AT FINDING X, SEE BELOW:
2x + 3 = 7
(Lets subtract 7 from both sides) 2x + 3 - 7 = 7 -7
2x - 4 = 0
(Add 4 on both sides)
2x - 4 + 4 = 0 + 4
2x = 4
(Divide both sides by 2)
2x/2 = 4/2
x = 2
AS LONG AS WE TREAT BOTH SIDES THE SAME WAY, THERE ARE DIFFERENT WAYS OF SOLVING FOR X. Try substituting x with 2 and see if the sides are balanced, if you do not know how to substitute, don't worry check the substitution page.

Video 2 Explanation

Question: Solve for x, given the linear equation -5 + 2x + 10 = 3x + x
-5 + 2x + 10 = 3x + x
Let's use our knowledge of simplifying both sides first.
We can simplify the first side, so
-5 + 2x + 10 = 2x + 5
We can simplify the second side, so
3x + x = 4x

So we can write
-5 + 2x + 10 = 3x + x
2x + 5 = 4xSolve to find x now.
2x + 5 = 4x
(Subtract 2x from both sides) 2x + 5 - 2x = 4x - 2x
5 = 2x
(Divide both sides by 2)
5/2 = 2x/2
2.5 = x

Try answering these questions:

3x - 3 = 10, solve to find the value x.
5y + 3 - 2y = 12, solve to find the value of y.
The length (cm) of the sides of a triangle are 2x, 2x and x. The perimeter of the triangle is 10cm, find x.

Answers:

x = 13/3
3
x = 2

This question requires you to form a linear equation to solve the question. ONCE you understand how to solve linear equations you can apply your knowledge and understanding to questions that do not directly showcase a linear equation.
A triangle has 3 sides with lengths 2x, 2x, and x. Perimeter of the triangle = 2x + 2x + xPerimeter of the triangle = 10cm
so
2x + 2x + x = 10
(Simplify each side)
5x = 10
(Divide both sides by 5)
5x/5 = 10/5
x = 2

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