Multistep Equations
Equations with Variables on Both Sides
Clearing Fractions
Special Cases
Real World Problems
100
Solve for p.
2(4p + 2) = 12
p = 1
100
Solve for x.
6x + 7 = 13 + 7x
r = -6
100
What could you multiply everything in the equation by to clear the fractions in this equation?
Any common multiple of 2, 8, 16.
100
Fill in the blank to create an equation that has one solution.
____x + 1 = 6x - 8
Anything other than 6 will work.
100
Derrick’s Dog Sitting and Darlene’s Dog Sitting are competing for new business. Derrick charges a one-time fee of $12.00 and an additional $5.00 per hour. Darlene charges a one-time fee of $18.00 and an additional $3.00 per hour. Write and solve an equation to find the number of hours for which the total cost will be the same for the two services.
12 + 5x = 18 + 3x
x = 3 hours
200
Solve for r.
r + 11 + 8r = 29
r = 2
200
-8 - x = -3x
x = 4
200
What multiple could you use to clear the fractions?
Any common multiple of 3 and 4 would work.
200
Fill in the blank so that the equation has infinitely many solutions.
3/4
200
Maria pays a yearly fee of $3 to her swimming club and $2 per lesson. Carmen pays a yearly fee of $5 and $2 per lesson. After how many lessons will Maria and Carmen have paid the same amount. Write an equation and explain your answer.
There is no solution. Carmen pays a higher yearly fee and pays the same per lesson. Therefore, Carmen's fees will always be higher.
300
Solve for y.
5y - 3(2 - y) = 10
y = 2
300
Solve for x.
-7x - 3x + 2 = -8x - 8
x = 5
300
Solve the equation.
x = 1
300
Fill in the blank to create an equation that has no solutions.
6x + 5 = 3 + _____
6x
300
Ms. Baumgartner draws a pair of supplementary angles and tells the class that the angle measures are (4x + 30)° and (2x + 6)°.
A. Write an equation to determine the value of x. Solve for x.
B.What does the larger angle measure? What does the smaller angle measure?
A. 4x + 30 + 2x + 6 = 180 or 6x + 36 = 180
x = 24
B. Larger Angle: 4(24) + 30 = 96 + 30 = 126o
Smaller Angle: 2(24) + 6 = 48 + 6 = 54o
400
Solve for m.
-13 = 5(1 + 4m) - 2m
m = -1
400
4n - 40 = 7(-2n + 2)
n = 3
400
Solve the equation.
m = 8
400
Complete the equation so that it has infinitely many solutions.
2h - 3(3 - h) + _______ = 5h - 8
1
400
A water tank holds 256 gallons but is leaking at a rate of 3 gallons per week. A second water tank holds 384 gallons but is leaking at a rate of 5 gallons per week. After how many weeks will the amount of water in the two tanks be the same?
256 - 3w = 384 - 5w
w = 64 weeks
500
If the perimeter of the rectangle is 96 feet, what are the length and width of the rectangular section?
Length: 39 feet
Width: 9 feet
500
Solve for m.
8m + 4(5m - 3) = 4(6m + 4) - 4
m = 6
500
Solve the equation.
x = 36/72
x = 1/2
x = 0.5
500
Complete the equation so that it has one solution.
-2(z + 3) - z = ______ - 4(z + 2)
Anything other than 1z or z
500
At Silver Gym, membership is $25 per month, and personal training sessions are $30 each. At Fit Factor, membership is $65 per month, and personal training sessions are $20 each. In one month, how many personal training sessions would Sarah have to buy to make the total cost at the two gyms equal?
25 + 30s = 65 + 20s
s = 4 sessions