Variables
What are two of the most common variables?
x, y, z, n
Evaluate.
3(2)+4
10
True or False?
4x = 2y when x=3 and y=6
True
True or False?
3x > 12 when x=4
A combination of numbers, variables, and operations that represents a value. Does not contain an equal sign.
What is an algebraic expression?
What is a variable?
Hint: "A letter" is not a sufficient answer.
A letter that represents an unknown or changing value.
Simplify when x=7
2x - 9
5
True or False?
9x - 17 = 7y + 14 when x=8 and 7=6
False
True or False?
2x - 4 < y when x=4 and y=6
True
A statement of equivalence of two values. Combines variables, numbers, operations, and an equal sign.
Describe a real life situation where you might use a variable.
Example: A football score where x represents the number of touchdowns.
Write the following expression.
The sum of 2x and 4
2x+4
Use the equation p=20f - 18 to find the value of p when f=7
122
Maria is planning to buy an $80 jacket. She will save the same amount of money for five weeks to afford the jacket. She hope's she will have some money left over, but she is unsure if she will.
What inequality represents this situation?
5x >/= 80
A statement that two values are not equal.
What is an inequality?
Identify the value that could be represented by a variable.
The price of gas is $2.75. I need to fill my tank before the work week starts!
The number of gallons of gas I need. /
The size of my gas tank.
Write the following expression.
The difference of x and the quotient of y and 2
x - y/2
Fourteen birds were sitting on a power line. When Weston blew a whistle, some of the birds flew away, leaving only five birds on the power line. Write an algebraic equation for this situation.
14-x=5
What is a situation that could describe the following inequality?
2x < 34
Example:
Kael brought suckers for his class. He did not have enough suckers to give two to each of his 17 classmates.
A number that multiplies a variable.
What is a coefficient?
Identify the values that could be represented by variables.
The gym has a $15 membership fee for every month you have it. It also charges $10 for each class you attend. At the end of the year, you spent a total of $400 at the gym.
x - the number of months you had the membership
y - the number of classes you attended
Equation: 15x+10y=400
Write an expression for the following scenario.
In the summer, Ms. Thomas drives for DoorDash. She charges a $5 fee for each trip and expects a $2 tip for each mile she must drive.
5+2x
3(x-2)+7=y+4
Solve for y when x=8
y=21
A movie theater has a budget of $120 to spend on snacks for a party. Popcorn costs $4 per bag, and drinks cost $3 each. The total cost of the popcorn and drinks cannot exceed the budget. Write an inequality that represents all possible combinations of popcorn and drinks the theater can buy.
4x + 3y </= 120
The process of removing unknown information with identified information.
What is substitution?