Vocabulary
What is an equation that sets two ratios equal to each other?
*a is to b as c is to d
Proportion
Solve the following proportion:
3 = x
5 10
6
Explain the steps to solve this equation:
2x + 1 = 11
Subtract 1 from both sides, then divide by two on both sides.
What sign is this:
>
Greater than
What operation would you use when you see the work and?
For example: You bought x amount of books and 3 CDs
addition
An equation where every variable represents a known value
(NO numbers and ALL letters)
Literal Equation
Find the Solutions:
|x| = 4
x = 4 and x = -4
What would be the first step in solving this equation:
2(2x - 1) - 3(3x - 1) = 5x + 1
Distribution
State the Negative Number Rule
When you multiply or Divide both sides by a negative you flip the inequality sign.
Let t be the number of tickets you are buying for a show. If the tickets cost $15 each and you spent $30 on concessions, how would you write this as a mathematical expression to show the amount you spent?
15t + 30
What is it called when we get the variable alone or by itself?
isolate
Explain the steps to solve this problem:
|x + 4| = 5
Write the two equations
Subtract 4 from both sides
Given the following formula:
F = 4a + 4b
What would be the first step if you were solving for b?
Subtract 4a from both sides.
How would you graph the following inequality? Include type of circle and direction.
x < 4
open and left
Andrew makes $30 an hour at his job, but he has to pay $5 for transportation. He wants to make at least $140 a day.
Write an inequality to show the possible hours he could work to reach his goal.
30h - 5 >= 140
Name this:
The non-negative value of x without regard to its sign. Shows the distance from zero.
Absolute Value
Ms. Alessandrini is buying lunch for her students. She knows that 4 hoagies can feed 12 people. She is planning on serving 75 people.
Write the proportion you would use to find the number of hoagies needed.
4 x
12 75
Given the following problem and work, determine the number of solutions are there and why:
3( x+ 2) - 2(x + 1) = x + 2
3x + 6 - 2x - 2 = x + 2
x + 4 = x + 2
No Solution
How would you graph the following inequality:
x < 1 or x > 4
<---------------------------------->
0 1 2 3 4 5
Open in opposite directions
Xfinity charges a $20 sign up fee and $75 per month for an unlimited data plan. Direct TV charges a $90 sign up fee and $45 per month.
Write the equation to find the number of months they would be the same.
20 + 70m = 90 + 45m
What is the smallest set in the Real Number System?
Natural Numbers
Chef Rita is cooking for a Sunday brunch. She knows that 40 pancakes can feed 6 people. She is planning on serving 30 people.
Write the proportion you would use to find the the number of pancakes needed.
6 30
40 x
Given the following problem and work, determine the number of solutions are there and why:
2(-2x - 1) + 3(3x + 1) = 5x + 1 d
-4x - 2 + 9x + 3 = 5x + 1
5x + 1 = 5x + 1
Infinitely many
Solve the following inequality
2x + 3 < x + 9
x < 6
Xfinity charges a $10 sign up fee and $50 per month for an unlimited data plan. Direct TV charges a $20 sign up fee and $40 per month.
Using the following equation, who would have more after 4 months?
Xfinity Direct TV
10 + 50m ___ 20 + 40m
Xfinity: 210
Direct: 180