Equation Experts
Solve for x: (-x/4) - 8.5 = -3.2.
x = -21.2
Solve for x: 7 - 3x < 22
x > -5
Write an inequality that represents the following sentence: Twelve less than the product of a number and -4 is less than 20.
-4n - 12 < 20
If -3x = 12, and x + y = 5, then what is the value of y?
x = -4, so y = 9
The room number Mr. Chatterjee's desk is in
What is 164 or the Hopper?
Solve for y: -2.5(y + 4) = 15.
y = -10
Solve for m: (-4m/5) + (1/5) > 2
m < -2.25, or (-9/4)
Ms. Poppleton has $50. She buys a book for $18.50 and wants to buy as many journals as possible with her remaining money. Each journal costs $3.75. Set up and solve an inequality to find the maximum number of journals she can afford.
3.75x + 18.50 < 50, so x = 8.4. She can't buy part of a journal, so 8 journals maximum.
Always, Sometimes, or Never: If you divide an inequality by a negative number, the solutions stay the exact same.
Never: The inequality's sign must flip if divided by a negative number, so the solutions will completely reverse.
Name one of the two universities that Mr. Chatterjee has attended.
What is Duke University or University of Washington?
Identify the error in this solution, correct it, and solve for x:
Step 1: (2x/3) - 6 = 10
Step 2: (2x/3) = 4
Step 3: 2x = 12
Step 4: x = 6
This student subtracted 6 from x instead of adding it.
Step 1: (2x/3) - 6 = 10
Real Step 2: (2x/3) = 16
Real Step 3: 2x = 48
Real Step 4: x = 24
Solve for b: -3(b - 2) > 12
b < -2
The temperature in a freezer is -2 degrees. It is cooling down at a consistent rate of 1.5 degrees cooler per hour. How many hours, h, will it take for the freezer to drop below -10 degrees? Set up and solve an inequality to answer this.
-2 - 1.5h < -10
h > 5.33, or 16/3
True or False: x = 4 is a solution for the inequality -2(x + 1) > - 12.
True
Substitution: -10 > -12 is true
Solving equation: x < 5 is all solutions. 4 < 5 is true!
What is geometry?
Solve for c: (3c-7)/5 = -4
c = -13/3, or 4.33333...
Solve for k: 0.5(4k - 10) + 3 < 8
k < 5
A rectangular picture frame has a perimeter of 84 inches. Its length is 6 inches longer than the width, w. Write and solve an equation to find the width of the picture frame.
2w + 2(w+ 6) = 84
2w + 2w + 12 = 84
4w + 12 = 84
4w = 72
w = 18 inches
Identify the error in this solution, correct it, and solve for x:
Step 1: -4(2x - 5) = 84
Step 2: -8x - 20 = 84
Step 3: -8x = 104
Step 4: x = -13
The student calculated -4 x -5 to be -20, instead of +20.
Step 1: -4(2x - 5) = 84
Real Step 2: -8x + 20 = 84
Real Step 3: -8x = 64
Real Step 4: x = -8
Mr. Chatterjee's favorite country to get in Geoguessr
What is Andorra?
Create and solve an equation that takes at least two steps to solve. It must have the solution x = -3, use division somewhere in the equation, and involve a decimal somewhere in the equation.
Various answers
Solve for x: 5x + 10 < 5x + 5
No solution. 10 is not less than 5.
Subscription service Netfrancis costs $10 a month, and requires you to pay $2 per movie you watch. Meanwhile, subscription service HBDORA Max costs $18 a month, but only costs $1 per movie you watch. If you only subscribed for one month, how many movies would you need to watch to make HBDORA Max cheaper than Netfrancis? Set up and solve an inequality.
10 + 2m < 18 + m
m < 8
Netfrancis is cheaper if less than 8 movies are watched. HBDORA Max is cheaper if watching 8 or more movies.
Write a word problem that could be modeled by the inequality 50 - 5x > 15. Account for all parts of the problem for full points!
Various answers
If you write Mr. Chatterjee's birthday out (MM/DD/YYYY) without the slashes, there will be a power of two contained within it without having to rearrange the numbers. What is that power?
2^9 = 512