GCF & Distributive Properties
Find the Greatest Common Factor (GCF) of 12 and 20.
4
Are x + x + x and 3x equivalent?
Yes
Solve for x: 2x + 10 = 20.
x = 5
Write the equation: Double a number plus five is fifteen
2x+5=15
Use the Distributive Property to expand 4(x + 5)
4x + 20
Which expression is equivalent to 2(3x + 4)?
A) 6x + 4
B) 6x + 8
B) 6x + 8
Solve for y: 3y - 5 = 16.
y = 7
A plumber charges $50 for a visit plus $25 per hour. The total bill was $125. Write the equation to find the hours (h).
50 + 25h = 125
Rewrite the sum 18 + 24 as a product using the GCF and the distributive property.
6(3 + 4)
Combine like terms to simplify: 5x + 7 + 2x - 3.
7x + 4
Solve for m: m/4 + 3 = 8.
m = 20
A plumber charges $50 for a visit plus $25 per hour. The total bill was $125. How many hours did the plumber work?
3 hours
Factor out the GCF to create an equivalent expression for 9x - 27
9(x-3)
Prove that 3(x + 2) is equivalent to 3x + 6
by substituting x = 4 into both.
Both equal 18
Solve for a: -2a + 8 = 2.
a = 3
You have $40. You buy a book for $10 and 6 identical pens. You have $6 left. Write and solve an equation to find the cost of one pen (p).
10 + 6p + 6 = 40
6p + 16 = 40
6p = 24
p = 4
The area of a room is 14x + 35. If the width is the GCF of the two terms, what are the length and width of the room?
Width = 7
Length = (2x + 5)
Write two different expressions that are equivalent to 20x + 10.
10(2x + 1) and 5(4x + 2)
Solve for x: 5(x + 2) = 40
x = 6
The perimeter of a rectangle is 40cm. The length is 12cm. Write and solve an equation to find the width (w).
P = 2W + 2L
40 = 2W + 2(12)
40 = 2W + 24
40 - 24 = 2W
16 = 2W W=8