Houston we have a problem
Austin has $145 in his savings account. He earns $36 a week mowing lawns. If Austin saves all of his earnings, after how many weeks will he have $433 saved?
145 + 36m = 433
x + 6 = 4
x = -2
What is the value of P in the following equation:
12p + 13 = 11
p = 2/3
_________________ is a symbol (such as a letter) that represents a number (i.e., it is a placeholder for a number).
A Variable
How can you tell when two quantities on a table are proportional?
When there is a constant unit rate between them ( a constant of proportionality)
It costs $12 to attend a golf clinic with a local pro. Buckets of balls for practice during the clinic cost $3 each. Write an equation to find the number of buckets you would be able to buy at the clinic if you have $30 to spend?
3b + 12 = 30
-2x = -6
x = 3
What is the value of x in the following equation?
2x + 10 = 20
x = 5
__________________ is a statement of equality between two expressions.
An Equation
What are the two characteristics of the graph of a proportional relationship?
A straight line that passes through the origin.
Mr. Thompson is on a diet. He is currently 260 pounds. On his diet, he loses 4 pounds per month. Write an equation that shows the number of months will he would have to diet to weigh 220 pounds?
260 - 4p = 220
4x = 8
x = 2
If 2x – 41 = 13, find the value of x
x = 27
To solve an equation we use ________________ ________________, which are operations that undo each other.
Inverse Operations
What is the equation of a proportional relationship?
y = kx
You spend half of your allowance at the movies, and you mow lawns over the weekend to earn an extra $12. If you currently have $25, how much allowance did you receive?
your allowance was 26 dollars
- x/5 + 42 = 57
x = -75
Solve: 3x + 5 = -7
x = -4
The inverse of multiply is ______________
Divide
What is the rule for adding integers that have different signs?
Subtract their absolute values and use the sign of the number with the greater absolute value
Lin is tracking the progress of her plant’s growth. Today it is 5 cm tall. If the plant grows 1.5 cm per day, after how many days will the plant be 20 cm tall?
It would take 10 days
x/4 + 5 = 9
x = 16
Solve for b to the nearest hundredth: 74b + 47 = 29
b = – 0.24
To solve an equation you must _________________ the variable
Isolate
What is the distance between two numbers on the number line called?
The absolute value