Question

How to Solve a variable in equations

Answer 1

1. X = 3
2. Y = -3
3. Z = -10
4. X = 100

Explanation:

You want to solve for the variable in each case:

1. x -3 = 0
2. y +3 = 0
3. z +20 = 10
4. x -40 = 60

Addition facts

When you first learned to count and to understand addition and subtraction, you could easily figure out the missing number based on your knowledge of addition facts:

___ -3 = 0 . . . . . the blank is filled with 3

___ +3 = 0 . . . . . the blank is filled with -3

In Algebra, we give the blank a name. We use a letter or symbol in place of the blank, and we call it a variable. It is still an unknown value until we figure out its value based on the rules of arithmetic and equality.

Properties of equality

Now that you know the properties of equality, you know that such equations can be solved by adding the same number to both sides of the equal sign:

___ -3 +3 = 0 +3 ⇒ ___ = 3

___ +3 -3 = 0 -3 ⇒ ___ = -3

This process also makes use of the idea of an additive inverse, and the fact that adding a number and its inverse gives zero (0), which is the additive identity element. That is, adding zero to anything does not change its value.

These ideas mean you can get rid of the unwanted constant on the same side of the equal sign as the variable. You do that by adding the opposite of that constant to both sides of the equation.

1. X -3 = 0

Add 3 to both sides:

X -3 +3 = 0 +3

X = 3

2. Y +3 = 0

Subtract 3 from both sides:

Y +3 -3 = 0 -3

Y = -3

3. Z +20 = 10

Subtract 20 from both sides:

Z +20 -20 = 10 -20

Z = -10

4. X -40 = 60

Add 40 to both sides:

X -40 +40 = 60 +40

X = 100