一元一次方程式 (One-Variable Linear Equation)

What can a linear equation be used in our actual life? Well, it could be very useful in solving a problem by transforming it into an equation, for instance:

Lily's grandmom's age is 7 times of Lily's. 9 years later, her grandmom's age is 4 times of her age.
How old is Lily and her grandmom now?

 Solution: 

let:

Lily is x years old,

her grandmother is 7x years old.

9 years later,

Lily is x+9 years old,

Her grandmother has an age of 7x+9.

since, grandmother's age is 4 times of Lily's age,

we can arrange the equation to:

4(x + 9 ) = 7x + 9 

solve x to get what is Lily's age:

NOTE: A(B + C) = AB + AC, WE GET:

4x + 36 = 7x + 9

7x - 4x = 36 - 9

3x = 27

x = 9

So, Lily is 9 years old, her grandmother is 63 years old.

As we can see from the example above, it is useful!
Before we go through the application of this one-variable linear equation,
Let's do some practice:

Solve x :

1. 5(x - 5) = 3(x - 1)

Solution: 

NOTE: A(B - C) = AB + AC, WE GET:

5x - 25 = 3x - 3    OR (-3 + 3x)
5x - 25 - 3x = -3
5x - 3x = -3 + 25 OR (25 - 3)
2x = 22
x = 22 / 2 = 11

NOTE THAT, 3x from RIGHT HAND SIDE MOVE TO LEFT HAND SIDE WILL GET A -3x
(FROM +3x to -3x),
while -25 FROM LEFT HAND SIDE MOVED TO RIGHT HAND SIDE WILL GET A +25

2.   x / 15 + x / 21 + x / 12 = 1

Solution: 

3. 

Solution: