Vocabulary
a letter in an algebraic equation
What is a variable?
Hadlee can run 10 feet in 2.5 seconds.What is her rate for f feet per second? Use the equation 2.5f = 10 to solve.
f = 4 feet
Using the inequality given, write 2 possible values for the variable z.
10 ≥ j
j can be any numbers that are 10 or less to make the inequality true.
What operation(s) do you use to isolate the variable? What does the variable equal?
4 + c = 17
c=?
subtraction
c=13
Tony and Bruce sell newspapers after school. Tony earns $13 more than Bruce. If Tony earns $25, how much money does Bruce earn? Write an equation and solve for the variable.
25 = b + 13
b = 12
What do we use this symbol for?
•
Multiplication
David reads a story and play. Th The play has 165 pages, which is five times as many pages as the story. Using the equation 5s = 165, find the number of pages in the story.
s = 33 pages
True or false: k = 3
4k > 16
False. k has to be greater than 4.
What operation(s) do you use to isolate the variable? What does the variable equal?
5s = 90
s = ?
Division
s = 18
Carson and Matthew run a race. Matthew takes 42 seconds to run the race. He is 7 seconds slower than Carson. How many seconds does Carson take? Write an equation and solve for the missing variable.
42 = c + 7
c = 35
What are inequalities used for?
What is to compare numbers and values?
Abby got a new 32 oz Hydro Flask. She paid $48 for it. How much did she pay (p) for each oz of room in the Hydro Flask? Using the equation 48 = 32p, solve for the unknown variable.
p=$1.50
Which values are solutions for the inequality given?
3; 7; 12.5; 8
2r + 1 < 18
r = 3, 7, and 8
What operation(s) do you use to isolate the variable? What does the variable equal?
45/y = 7.5
Multiplication
y = 6
Miles Morales age is Peter Parker’s age divided by 2. If Miles’ age is 14 years old how old is Peter? Write an equation and solve for the variable.
14 = m/2
m = 28
Peter Parker is 28 years old.
3z
^
What happens where the arrow is indicated?
Solve when z=33.3
3 and z are multiplied
3z
3 (33.3) = 99.9
Aaric has a book that has 328 pages in it. He reads the book in 4 days. What is his rate for pages per day (p)? Using the equation p = 328/4, solve for the variable to figure out how many pages he read per day.
p = 82 pages
Look at the inequality below. Based on the inequality, draw a graph to represent the situation.
h ≤ 2.5
Closed circle, arrow starting on 2.5 and pointing to the left.
What operation(s) do you use to isolate the variable? What does the variable equal?
c + c =9
c=?
Division and addition
c = 4.5
Michela went to the mall and spent $90 for shoes and clothes. She spent $56.80 on shoes. Write an equation that can be used to find out how many dollars d she spent on clothes.
d = 90 - 56.80 or 90 = d + 56.80
Using words and numbers, explain the difference between an algebraic expression in an algebraic equation.
An algebraic expression is a math problem that has at least one variable and no =.
m + 7
an algebraic equation has at least one variable that can be isolated to find what it is equal to. has a =
m + 7 = 15
m = 8
Noah's family is driving from their house to Chicago. They are driving in a car that goes 20 miles per gallon (MPG) of gas. They drove a total of 2,150 miles. How many gallons of gas, g, did they use? Write an equation and solve for g.
Equation: 2,150/20 = g or 20g=2,150
g=107.5 gallons of gas
Read: Patrick has played at minimum 40 hours of The Legend of Zelda in this past week. Write an inequality and graph the inequality to represent this situation.
h ≥ 40
Closed dot on the 40 with the arrow pointing to the right.
What operation(s) do you use to isolate the variable? What does the variable equal?
8w + 6 - 2 = 5w + 13
Division, subtraction, and addition
w = 3
Read: Chromebook computers have 1/4 of the gigabytes of storage that Apple MacBooks have. Chromebooks have 20 gigabytes of storage. in order to solve, Natasha and Clint each write an equation to find how many gigabytes of storage an Apple MacBook has. Looking at the equations below, determine if one, both, or neither are correct.
Natasha: 20 = 1/4z
Clint: 20 = z/4
Both Natasha and Clint are correct. When you solve for both equations, the variable z equals 80.
z = 80