Expanding/Factoring Expressions
Use the distributive property to simplify:
2(3x + 5)
6x + 10
Combine like terms:
13x + 4 - 8x
5x + 4
4 + 5x
Solve the following by isolating the variable:
2 + x = 8
x = 6
Solve the following by isolating the variable:
2x + 4 = 8
x = 2
Combine like terms to solve:
4x - 7x + 12 = 24
x = -4
Factor this expression:
15x + 5
5(3x + 1)
Combine like terms:
10b - 4x + 6x - 21
10b + 2x - 21
Solve the following by isolating the variable:
y - 5.2 = 8.1
y = 13.3
Solve the following by isolating the variable:
1/3y - 7 = 14
y = 630
The chess club has 50 members. They want to raise $680 for a trip to a competition. The school will give $130. How much must each member pay?
Each member must pay $11.
-4(3x - 6)
-12x + 24
1.5x + 3y + 2.8x + 4.2y
4.3x + 7.2y
Solve the following by isolating the variable:
h/13 = 3.5
h = 45.5
Solve the following by isolating the variable:
b/5 + 3 = 11
b = 40
Rashida owns a bike rental company. She charges an initial fee of $10 for each rental and an hourly rate of $4. A customer paid $34 for a bike rental. What equations could be used to find the number of hours, x, the customer rented the bike?
10 + 4x = 34
18 - 4y
2(9 - 2y)
Simplify using the distributive property. Then combine like terms.
3(1.2x + 7) + 5x
8.6x + 21
Solve the following by isolating the variable:
0.25x = -10
x = -40
Janet went to the store and bought three shirts as well as a pair of boots. Each shirt costs the same amount. The boots were $32.85. If Janet spent a total of $71.10, what equation can be used to find the cost of each shirt?
3s + 32.85 = 71.10
Jane has 6 more than half the number of pairs of shoes that Mercedes has. Write an expression for this.
1/2x + 6
0.5x + 6
Use the distributive property to simplify then solve.
4(2b - 5) = 12
8b - 20 = 12
b = 4
Simplify using the distributive property then combine like terms:
4.4y + 8.3x + 2(5.1x + 4)
18.5x + 4.4y + 8
Write the one -step equation and then solve:
Mareese can spend $40 total to ride a bus. Each time she rides, it is $2.25. How many times can Mareese plan to ride the bus on that budget?
2.25r = 40; r = 17.7
She can plan to ride the bus 17 times.
Two years of local Internet service costs $685, including the installation fee of $85. What is the monthly fee? Write an equation and solve.
24m + 85 = 685
m = 25 months
Juma earns $12.50 for each newspaper subscription he sells. He also earns a $50 base salary each week. If he wants to earn $400 next week, how many newspaper subscriptions does he need to sell? Write an equation and solve.
12.50n + 50 = 400
n = 28 subscriptions