Vocabulary
What is a letter called in math? x, y, a, b
Variable
Solve the equation and show your work: x+7=12
x = 5
Solve the inequality and graph it on a number line: x−5<2
x < 7
show graph
Write an inequality and solve: “A bookstore sells notebooks for $4 each. If you have $25, what is the greatest number of notebooks you can buy?” (Let n = number of notebooks.)
4n < 25 or 25 > 4n
n < 25/4 =6.25 (N < 6.25)
Number of whole books you can buy is 6
What word is used for doing the opposite?
Inverse
Solve the equation and show your work: x−9=5
X = 14
Solve the inequality and graph it on a number line: 5x > 20 (greater than or equal to)
x > or equal to 4
show graph
Write the inequality and solve: “Sara needs more than 10 liters of paint. Each can holds 3 liters. How many whole cans must she buy?” (Let c = number of cans.)
10 < 3c or 3c > 10
c > 10/3 =3.333 (C > 3.333)
Whole cans needed is 4
Explain the difference between an equation and an inequality in one or two sentences.
Equation has =
Inequality has <, >, or equal to
Solve the equation and show your work: -4x=20
x = -5
Determine whether the number x=3 is a solution to the inequality x+4>6. Explain why or why not.
Yes 3 is a solution
Because 3 > 2 (x > 2)
Write an inequality for this sentence and solve: “A pizza place charges $8 plus $2 per topping. You have at most $14. How many toppings can you afford?” (Let t = number of toppings.)
Write the inequality and then solve
8 + 2t ≤ 14
t ≤ 3
What does it mean to “solve” an inequality? How is checking a solution different (or the same) as for equations?
To solve an inequality is to find all values that make it true. Checking is substituting a value to see if the statement is true — same idea as with equations.
Solve the equation and show your work: x/3 =1.5
x = 4.5
Solve the inequality: x/4 ≤ 2.5
Is X = 15 a solution to the inequality?
x ≤ 10
No because 15 is not less than 10
Write and solve: “A gym membership costs $20 per month plus a one-time fee of $15. You HAVE $95. For how many months m can you pay?”
Write the equation and solve
20m + 15 = 95
20m = 80
m = 4
You can go for 4 months paid.
Explain why multiplying or dividing both sides of an inequality by a negative number changes the direction of the inequality sign. Give a short numeric example.
It is to keep the statement true
Solve the equation and show your work and check your solution: −2x+5=15
x = -5
-2(-5) + 5 = 15 (True)
Explain how you would test is a solution works for an inequality? What are you doing to make sure it is?
Multi-step: “A group is buying tickets for a field trip. Each ticket costs $9. They also need to reserve a bus for $75 total. If their budget is $200, what is the maximum number of tickets t they can buy? Write an inequality, solve it, and explain how you found the maximum whole-number of tickets.”
9t + 75 ≤ 200
9t ≤ 125
t ≤ 13.888
So you can buy a maximum of 13 tickets to stay under your $200.