Linear Equations (One Variable)

Linear Equations (One Variable)

How to solve linear equations (one variable) problems: examples and their solutions.

Example 1

Solve the equation. x + 2 = 3

Solving an equation is finding the value of x
that makes the equation true.

So just think x + 2 = 3
as □ + 2 = 3.

We all know that □ = 1.

Solving an equation is that simple.

Then let's see, rather than just guessing the x,
how to find the value of x systematically.

To remove 2 on the left side,
write, the opposite of +2, -2 on both sides.

Then x = 3 - 2,
so x = 1.

This is the answer.

To check the answer,
put the answer into the x
and see if the equation is true.

1 + 2 = 3
is true.

So x = 1 is the right answer.

Example 2

Solve the equation. y - 1 = 4

To remove -1 on the left side,
write +1 on both sides.

Example 3

Solve the equation. 7z = 35

To remove the coefficient 7,
divide 7 on both sides.

Example 4

Solve the equation. -k/7 = 6

To remove both (-) sign and 7,
multiply (-7) on both sides.

Example 5

Solve the equation. 5x + 8 = -13 + 2x

To solve this equation,
you should move +2x on the left side
and move +8 on the right side.

But, instead of writing -8 and -2x on both sides,
use this trick to solve the equation faster:

Move +8 to the other side
and change its sign (-8).

By the same way,
move +2x to the other side
and change its sign (-2x).

This trick will surely save your time
when solving equations.

To remove the coefficient 3,
divide 3 on both sides.

Example 6

Solve the equation. a - 3(a - 2) = 8

To solve the parentheses,

first mutiply [-3] and [a] (blue),
then multiply [-3] and [-2] (purple).

Move +6 to the right side
and change its sign (-6).

To remove the coefficient -2,
divide -2 on both sides.