Solve That Equation
Solve 4x - 5 = 3.
x = 2
Akira plans to cut paper baseballs with a diameter of 3.2 inches. When figuring out how much paper she needs, she rounds the diameter to 3 inches. Does her choice make sense? Why or why not?
No! She will not have enough paper if she rounds down.
What is a "literal equation"?
An equation with multiple different variables in it.
What is the first step in solving the equation below?
9(x + 5) = 7 + 5(7x - 8)
Distribute the 9 and the 5. (Distributive Property)
What is a constraint?
A restriction that limits the possible solutions to a problem.
Solve 0.1c + 0.2c = 6
c = 20
The school store sells "n" notebooks and "f" folders. The equation t = 2.5n + f represents the total amount earned, t, from selling notebooks and folders. What does the term "2.5n" represent?
The amount earned from selling "n" notebooks for $2.50.
A museum wall has a total area of 150 square feet. The wall is partially covered by 23 pieces of art, all in identical square frames. The remaining 58 square feet of wall remains uncovered. Name a quantity that could be represented by a variable.
The area of a square frame, the height of the museum wall, the length of a square frame, etc.
How would you justify going from this step:
9x + 45 = 35x - 33
to this step:
9x + 78 = 35x ?
Addition Property (add 33 to both sides)
Provide an example of the subtraction property of equality.
Answer will vary (a situation where something is being subtracted from both sides of an equation)
Solve -(4x - 1) = 2x + 5 - 3x
x = (-4/3)
The school store sells "n" notebooks and "f" folders. The equation t = 2.5n + f represents the total amount earned, t, from selling notebooks and folders. What constraints are there on the value of "f"?
Since "f" represents the number of folders sold, it cannot be a negative number or a fraction/decimal.
Solve the equation for "h":
V = (1/3)lwh
h = (3V)/(lw)
How would you justify going from this step:
6x = 48
to this step:
x = 8 ?
Division Property (divide both sides by 6)
Solve x^2 = 36
Positive or negative 6.
Solve (2x + 6)/3 = 2(x - 2)
x = 4.5
The school store sells "n" notebooks and "f" folders. The equation t = 2.5n + f represents the total amount earned, t, from selling notebooks and folders. How would you represent the constraint on the value of "t", using an inequality?
The total amount earned cannot be a negative number, so t ≥ 0
Write an inequality to represent the situation: Jack must be at least 45 inches tall to ride the rollercoaster.
J ≥ 45
How would you justify going from this step:
5y - 3 + 2y = 4y - 6
to this step:
7y - 3 = 4y - 6
Combine Like Terms
The side length is 8 feet. It cannot be a negative number, which is why -8 feet is not an option.
Solve the following equation for y:
6x - 3y = 18
y = 2x - 6
How would you justify going from this step:
(1/3)x = 6
to this step:
x = 18 ?
Multiplication Property (multiply both sides by 3)