Solving Equations
Checking Solutions to Inequalities
Graphing Inequalities
Inequality Word Problems
Just for Fun!
100
5x+1=2x+3
Fill in the blanks to write an equivalent equation.
3x + ____ = _____
3x+1=3
100
Is x=2 a solution to the inequality below? How do you know?
3x-1>0
Yes! When you plug in 2 for x, it simplifies to 5 is greater than 0 which is true.
3(2)-1>0
5>0
100
Would the graph of the inequality have a dashed or solid line?
How do you know?
y<3x+1
This graph would have a dashed line because the inequality does not have "or equal to"
100
A student has 240 minutes this week to spend on math practice and reading. Each math practice set takes 20 minutes, and each reading chapter takes 30 minutes. Let m represent the number of math practice sets. Let r represent the number of reading chapters.
- Write an equation that represents the number of math practice sets and reading chapters that use exactly 240 minutes.
20m+30r=240
100
What is the capital of Maryland?
Annapolis
200
Solve for x.
7=3x+2x-3
x=2
Combine Like Terms:
7=5x-3
Solve for x.
10=5x
2=x
200
Is (0,0) a solution to the inequality below? How do you know?
3x+2y<-5
No! If you plug in 0 for x and 0 for y, it simplifies to 0 is less than -5 which is not true.
3(0)+2(0)<-5
0<-5
200
Maria plugged in (0,0) to the inequality and discovered it was NOT a solution.
Which region should she shade? How do you know?
She should shade region A BECAUSE (0,0) does not work and (0,0) is in region B.
200
A student has 240 minutes this week to spend on math practice and reading. Each math practice set takes 20 minutes, and each reading chapter takes 30 minutes. Let m represent the number of math practice sets. Let r represent the number of reading chapters.
- Write an inequality that represents the number of math practice sets and reading chapters that use 240 minutes or less.
20m+30r<=240
200
What is the largest ocean on earth?
The Pacific Ocean
300
Solve for x.
8=2x-4+x
x=4
Combine Like Terms:
8=3x-4
Solve for x.
12=3x
4=x
300
Is (2,3) a solution to the inequality below? How do you know?
3x-4y>1
No! If you plug in 2 for x and 3 for y, it simplifies to -6 is greater than 1 which is not true.
3(2)-4(3)>1
-6>1
300
Luke plugged in (0,0) to the inequality and discovered it is a solution.
Which region should he shade? How do you know?
He should shade region A because (0,0) is a solution and (0,0) is in region A.
300
A school club has $300 to buy pizzas and sandwiches for a fundraiser. Each pizza costs $12, and each sandwich costs $6. Let p represent the number of pizzas. Let s represent the number of sandwiches.
- Write an equation that represents the number of pizzas and sandwiches the club can buy if it spends exactly $300.
12p+6s=300
300
What country has won the Men's World Cup the most times?
Brazil
(5 times)
400
Solve for x.
3(x+2)=5x-10
x=8
Distribute:
3x+6=5x-10
Move Variables to 1 side:
6=2x-10
Solve for x:
16=2x
8=x
400
Write the coordinates of ONE solution to the inequality below.
5x-4y>0
Many answers!
(1,0) , (2,0) , (1,-3) , (1,1) , (5,5). . .
Any solution where y<(5/4)x
400
Which graph represents all the solutions to
2x+y>=4
Graph B
If you plug in (0,0) you get
2(0)+(0)>=4
0>=4
Which is not true, so you have to shade the region that does not include (0,0)
400
A school club has $300 to buy pizzas and sandwiches for a fundraiser. Each pizza costs $12, and each sandwich costs $6. Let p represent the number of pizzas. Let s represent the number of sandwiches.
- Write an inequality that represents the number of pizzas and sandwiches the club can buy if they spend $300 or less.
12p+6p<=300
400
How much does the average cloud weigh?
Around 1 million pounds
500
Solve for x.
7x-1=2(x+2)
x=1
Distribute:
7x-1=2x+4
Move Variables to 1 side:
5x-1=4
Solve for x:
5x=5
x=1
500
Write the coordinates of TWO solutions to the inequality below.
6x-2y<0
Many answers!
(0,1) , (0,5) , (1,10) , (-1,1) , (-5,5). . .
Any solution where y>3x
500
Which graph represents all the solutions to
2x-3y>12
Graph A
If you plug in (0,0) you get
2(0)-3(0)>12
0>12
Which is not true, so you have to shade the region that does not include (0,0)
500
A school club has $300 to buy pizzas and sandwiches for a fundraiser. Each pizza costs $12, and each sandwich costs $6. Let p represent the number of pizzas. Let s represent the number of sandwiches.
The club decides to buy 10 pizzas. How many sandwiches can they buy?
30 sandwiches or less
At most 30 sandwiches
12(10)+6s<=300
120+6s<=300
6s<=180
s<=30
500
What is a group of porcupines called?
A prickle