Inverse Operations
What operation should I use to solve? What is the value of n?
n/7 = 4
Multiplication n = 28
Is 7 a solution for 4p + 3 + 5 = 36
Yes!
4(7) + 3 + 5 = 36
28 + 8 = 36
36 = 36
The independent variable is typically put on which axis?
The x-axis!
The area of Floria is 65,758 mi². It is 6,333 square miles less than the area of Georgia. Write and solve and equation to find the area of Georgia.
65,758 = g + 6,333
g = 59,425 mi²
Write an equation to match the statement:
The output is 4 less than the input.
y = x - 4
What operation should I use to solve? What is the value of n?
47.3 = n + 15.3
Subtraction! n = 32
Solve for k:
6 + 2k + 4 = 20
6 + 2k + 4 = 20
2k + 10 = 20
2k = 10
k = 5
Is (3, 9) a solution of the equation, y = 3x + 1?
No!
9 = 3(3) + 1
9 = 9 + 1
9 X 10!
You plan to run 4.25 miles. So far, you have run 3.1 miles. How far are you from reaching your goal? Write an algebraic equation and solve.
Let m = miles left.
4.25 = m + 3.1
m =1.15 miles
Write an equation to match the statement:
4 is one-fourth of a number z.
4 = 1/4z
What operation should I use to solve?
Which operation should I use to check?
15n = 54
Divide by 15 to solve.
Substitute your value for n and multiply to check.
Is 2.5 a solution for 20/x = 8?
Yes! 20/2.5 = 8!
What are the next three ordered pairs for the rule y = 4x - 3 if the x values are 3, 4 and 5?
(3, 9) (4, 13) and (5, 17)
Emily is decorating 45 tables with 6 purple flowers and 2 yellow flowers. Write an equation that represents the total number of flowers (f) Emily will need.
Let f = flowers
f = 45(6 + 2)
An equilateral triangle has a side value of 2x inches. What is the perimeter of the triangle is x = 2.5 inches?
P = 2x + 2x + 2x
P = 6x
P = 6(2.5)
P = 15 inches
How many inverse operations do I need to solve? What are they?
25n + 5 = 55
Two! Subtraction and division
What is the value of n?
2n + 5 = 8n - 1
n = 1
Write an equation to show the relationship between x and y in the following ordered pairs:
(2, 8)
(3, 12)
(5, 20)
y = 4x
After 6 games, 3 football teams were eliminated from the tournament. There are 15 teams left. Write an equation to show the amount of teams that were in the tournament to begin with (t) and solve.
t - 3 = 15
t = 18
Solve for x:
5 + 4x − 7 = 4x − 2 − x
5 + 4x − 7 = 4x − 2 − x
4x - 2 = 3x - 2
4x = 3x + 0
x = 0
In the equation: 3x + 9 - 2 = 43, which inverse operation comes LAST? Solve for x.
Division!
3x + 9 - 2 = 43
3x + 7 = 43
3x = 36
x = 12
Solve for x:
−3(4x + 3) + 4(6x + 1) = 43
−3(4x + 3) + 4(6x + 1) = 43
−12x - 9 + 24x + 4 = 43
12x - 5 = 43
12x = 48
x = 4
Write an equation to express the relationship between x and y:
(2, 5)
(4, 10)
(6, 15)
(8, 20)
Would (9, 22.5) be a solution?
y = 2.5x
Yes! 22.5 = 2.5(9)
22.5 = 22.5
You bake x cookies. Your best friend bakes y cookies. Your best friend bakes three less than four times the amount of cookies you bake.
a) Write an equation to show the cookies your friend bakes.
b) If you bake 12 cookies, how many does your friend bake?
c) If your friend bakes 33 cookies, how many did you bake?
a) y = 4x - 3
b) y = 4(12) - 3
y = 48 - 3
y = 45 cookies
c) 33 = 4x - 3
36 = 4x
x = 9 cookies
Lily is saving money to buy a new bicycle. She already has $25 saved. Each week, she saves an additional $8 from her allowance. After a certain number of weeks, she finally has $81 saved. How many weeks did it take Lily to save enough money for her bicycle?
Write an algebraic equation and solve!
Let w = weeks
$8w + $25 = $81
$8w = $56
w = 7 (weeks)