Vocabulary
The parts of an expression that are added or subtracted
Term
A number increased by 7 is 19.
x + 7 = 19
2x + 5 = 17
x = 6
Maria has $5 and earns $3 per hour babysitting. She has $23 total. How many hours did she babysit?
3x + 5 = 23
x = 6 hours
What are the operations that "undo" each other called?
Inverse Operations
Terms with the same variables raised to the same exponents
Like Terms
3 times a number minus 6 is 15
3x − 6 = 15
3x − 4 = 11
x = 5
A streaming service charges a $6 monthly fee plus $2 per movie rental. If the total bill was $18, how many movies were rented?
2x + 6 = 18
x = 6 movies
To solve 5x − 7 = 12, what is the first step?
Add 7 to both sides
A symbol used to represent a quantity (or unknown) that can change
Variable
8 more than 4 times a number is 36
4x + 8 = 36
0.5x + 4 = 19
x = 30
A furniture store offers a one-time $55 discount when you buy a set of chairs. Will buys a set of 6 chairs and pays $455 in total. What is the regular price of each chair?
6c - 55 = 455
c = $85
To solve (x/4) = 10, what is the inverse operation you must use?
Multiplication
The number that is multiplied by the variable in an algebraic expression.
Coefficent
Three-fourths of a number plus 5 equals 17
(3/4)x + 5 = 17
(1/4)x + 3 = 11
x = 32
A taxi charges a $7 starting fee plus $2.50 per mile. If the total cost of the ride was $27, how many miles were driven?
2.5x + 7 = 27
x = 8 miles
What is the first step when solving the following;
-(x + 7) = -15
Distribute -1 to both x and 7
A number on its own that does not change
Constant
6 more than half a number is 20
x/2 + 6 = 20
x/3 + 4 = 9
x = 15
Each student in an art class uses 1/2 a pound of clay for a project. The teacher also uses 3 pounds of clay for a demonstration. If the total amount of clay used was 15 pounds, how many students are in the class?
(1/2)x + 3 = 15
x = 24
Name the property that allows you to change 3(x +2) =12
The Distributive Property