3.1 – solving equations by using addition and subtraction
TRANSCRIPT
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