Download 1.3 Solving Equations

1.3 Solving
Equations
Translating words in to math
and Solving equations
Words into math
A few ways of saying Add; more, plus,
increase by, sum
To Subtract: less, minus, decreased by
To Multiply: times, the product, twice, half
To Divide: the quotient, would half also be a
division statement?
Square, Cube,…… the list goes on and on.
A number means some variable
3 more than a number, would be 3 + x
if I want x as the variable.
Six times the cube of a number. 6x3

The square of a number decreased by the product
of 5 and the number
x2- 5x
Twice the difference of a number and 6
2(x – 6)
How about the other way, math into
words
14 + 9 = 23
 Fourteen added to nine is twenty three

19 = 7y – 2
 Nineteen is seven times a number minus 2

Properties of Equality
Addition property of equality.
 You can add the same number to both
side of an equation.

Multiply property of equality.
 You can multiply the same number, except
zero, to both side of an equation.

Here is how you would use the
properties
x – 8 = 12
add 8 to both side of the equation.
x – 8 + 8 = 12 + 8
x + 0 = 20
so x = 20
1
x8
3
Multiply both side by 3, the
fraction reduces. Thus x = 24
Now for a problem with more then
one step
53 = 3(y – 2) – 2(3y – 1)
distribute
53 = 3y – 6 – 6y + 2
Add like terms
53 = - 3y -4
Add 4 and divide by – 3
57 = -3y
- 19 = y or y = - 19
We can use the properties to move
equation around
Distribute property
 Add like terms
 We use the addition property to move
terms from side to side
 Multiplication property to solve the
equation.

To change a formula around
Why would we do this to a formula?
Given A  1 b  b h
1
2
2
Solve for h
To clear fractions, we can multiply by the
common dominator, which in this case is 2
2 A  b1  b2 h
We can go two ways at this point
We can distribute or just divide
 I choose to divide by b1  b2 

Giving Us
2A
h
b1  b2 
Homework

Page 24 – 26
# 19 – 23 odd, 29 – 39 odd, 41-46,47-51 odd,
57 – 60, 65, 67