3.1 – SOLVING EQUATIONS BY USING ADDITION AND SUBTRACTION

3.1 – SOLVING EQUATIONS BY USING

ADDITION AND SUBTRACTION

Addition Property of Equality:

If the same number is added to equal numbers, the results are equal.

If , then 2 2x y x y

If , then 100 100a b a b

Subtraction Property of Equality:

If the same number is subtracted to equal

numbers, the results are equal. If , then 2 2x y x y

If , then 100 100a b a b

Property of Opposites:

If you add opposite numbers, you will get

zero.

0x x

5 5 0 or 5 5 0 or 5 5 0

4 4 0y y

Solving Equations:

Think of an equation as a balance scale.

In order for the scale to remain balanced, both

sides of the scale must be the same at all times.

Solving Equations:

Think of an equation as a balance scale.

What must the unknown square weigh?

12

12x

Solving Equations:

Think of an equation as a balance scale.

What must the unknown rectangle weigh?

- 2

2x

Solving Equations:

If you add or subtract a number from one

side of the equation, the scale is no longer

balanced.

Solving Equations:

Think of an equation as a balance scale.

What must the unknown square weigh?

12

+2

2 12 10x x

Solving Equations:

Think of an equation as a balance scale.

What must the unknown square weigh?

12

- 2

2 12 14x x

Solving Equations:

Therefore, if you add or subtract a number

from one side of the equation, you must

balance it by adding/subtracting the same

number from the other side of the equation.

Solving Equations:

When you solve an equation, you are solving

for the value of the unknown variable.

If you are solving for this equation, you are

looking for the value of x. Get x by its itsy

bitsy self.

4 10x

Solving Equations:

A positive number will become a zero when

you subtract the same number.

A negative number will become a zero when

you add the same positive number.

4 4 0

4 4 0

Solving Equations:

Solve this equation: how do you clear a

positive 4? 4 10x

Solving Equations:

Solve this equation: subtract 4

from both sides of the equation

4 10

4 4

6

x

x

Try these:

Solve this equation: how do you clear a

positive 6?6 13x 6 3x

Solving Equations:

Solve this equation: how do you clear a

negative 4? 4 10x

Solving Equations:

Solve this equation: add 4 from both sides of

the equation

4 10

4 4

14

x

x

Try these:

Solve this equation: how do you clear a

negative 6?6 13x 6 3x

Solving Equations:

Solve this equation: Remember to solve for

positive x, not negative x.

4 10x

Solving Equations:

Solve this equation: Remember to solve for

positive x, not negative x. Subtract 4 to both

sides

Since x is negative,multiply both sides by negative 1

4 10

4 4

6

1 6 1

6

x

x

x

x

Try these:

) 6 13 ) 3 3a x b x

Word Problem Equations:

1) Four more than a number is eleven.

2) Three less than a number is negative ten.

4 11x

3 10x