Equation Fun
Solve the equation and check your solution
3x=72
x=24
3(24)=72
72=72
Solve the equation. Simplify if possible. Check your solution
x - 3/4 = 5 3/4
x=6 1/2
6 1/2 -3/4 = 5 3/4
6 2/4 -3/4 = 5 3/5
5 3/4 = 5 3/4
Amauri made and sold 15 brownies last week. If he made $60, how much did each brownie cost? Define the variable, write an equation, solve, and check your work.
c=cost of 1 brownie
15c=60
c=4
15x4=60
60=60
A car travels 60mph (miles per hour).
x=hours
y=distance
Which is the independent and dependent variable. Explain.
X, hours, is the independent variable
y, distance, is the dependent variable
The distance is dependent because it relies on the number of hours spent driving.
Solve and graph the inequality.
-7 +x <-15
x<-8
Graph-open dot on -8, arrow moving toward the left away from 0
Solve the equation and check your solution
8.5+x=-7
x=-15.5
8.5 + (-15.5) = -7
-7=-7
Solve the equation and check your solution
x/6 = -5.5
x=-33
-33/6 = -5.5
-5.5=-5.5
Emilia went to a garage sale and decided to buy some books. Each book cost $2. She liked so many of the books that she went over her $10 budget.
Let x represent how many books Emilia bought. Write and solve an inequality to describe the situation. Then solve.
2x>10
x>5
Leo spends $5 per week on music. Make a table that shows how much he spends over 4 weeks.
a. Write an equation that determines the dollars spent per week.
b. Determine how much he spent over 6 weeks.
a. d=5w
b. $30
Solve and Graph the inequality
5x+3x >108
x>13.5
Graph-open dot on 13.5, arrow goes to the right toward 15
Solve the equation and check your solution.
3x-56 = 7
x=21
3(21) - 56 = 7
63-56=7
7=7
Solve and graph the inequality
x/4 + 15 > 3
x>-48
Graph - open circle on -48, arrow pointing toward the right.
A taxi charges $1.75 plus a fee of $0.75 for each mile traveled. The total cost of a ride, without a tip, is $4.75. How many miles is the trip? Use m for the number of miles traveled.
Define the variable, write an equation, solve then equation, then check your work.
m=miles driven during the trip
1.75+0.75x = 4.75
m=4
1.75+0.75(4)=4.75
1.75+3 = 4.75
4.75=4.75
Sally sets up a booth at the bake sale and sells cupcakes. Each day, she makes $50.
x=number of days she sets up a booth
y=total money earned
Which variable is the dependent variable? Which is the independent variable? Why?
y, money earned, is the dependent variable.
The amount Sally earns relies on how many days she sets up at the bake sale.
Solve and graph
-5x<100
x>-20
Graph- open dot on -20, arrow goes to the right toward positive numbers
Solve the equation and check your solution
-5m - 8.5 = 8.5
m=-3.4
-5(-3.4) -8.5=8.5
17-8.5=8.5
17=17
Solve the equation and check your solution
3/4x - 5 = -3
x= 2 2/3
3/4(2 2/3) - 5 = -3
3/4(8/3)-5=-3
3/4(16/6)-5=-3
48/24 -5= -3
2-5=-3
-3=-3
A home repair crew charges seventy-five dollars per day plus two hundred fifty-five dollars for each hour the crew works. One day the crew works c hours and charges a total amount of one thousand, six hundred five dollars. How many hours does the crew work?
Define the variable, write an equation, solve and check your solution
c=hours the crew works
75+255c = 1,605
c=6
75+255(6)=1605
75+1,530=1,605
1,605 = 1,605
Shelby walks at a constant rate. The equation that represents this relationship is d=4t, where d is the distance in miles and t is the time in hours.
a. What does the constant 4 tell you about Shelby?
b. What question is answered by the equation d=4(32)?
a. She walks at a rate of 4mph
b. How many miles she has walked after 32 hours.
Write the inequality based on the situation below. Solve and graph your inequality.
8.4 less than times a number is at most 30
3x-8.4 ≤ 30
x ≤ 7.2
Graph-closed dot on 7.2 with arrow moving to the left
Solve the equation below, then check your solution.
-x + 9.38 = 2
x=7.38
Solve and graph the inequality below
-3/4x + 8 > 3
x<6 2/3
Graph- open dot on 6 2/3, arrow goes to the left
The dance committee of Pine Bluff Middle School earns $72 from a bake sale and will earn $4 for each ticket they sell to the Spring Fling dance. The dance will cost $400. At least how many tickets will need to be sold to cover the cost of the dance?
Shane wrote the inequality 72+4t < 400.
Is this inequality correct? If not, correct it, then solve and graph the inequality.
72+4t ≥ 400
t≥82
Graph-closed dot on 82, arrow goes to the right
Emma decided to start a snow globe collection. She started with 3, and every year she added one more.
a. Create a table showing the growth in Emma's now globe collection over 5 years.
b. Write an equation to determine the number of snow globes she has after y years.
c. How many years will it take her to get 25 snow globes.
a. x y
1 4
2 5
3 6
4 7
5 8
b. s=y+3
c. 22 years
Solve and graph
6 - 1 1/5x ≥ 12
x ≤ -5
Graph- closed circle, arrow moving to the left.