ADD & SUBTRACT LINEAR EXPRESSIONS
5d – 7 – d + 4
4d - 3
Simplify the expression by distributing and then combining like terms.
5(b + 6) - 3b
2b + 30
-5x + 9 = 24
x = -3
5(b + 6) = 18
b = -2.4
A home improvement store advertises 60 square feet of flooring for $287.00, including an $80.00 installation fee. Write an equation to represent the cost of one square foot of flooring and solve.
Equation: 80 + 60x = 287
Answer: $3.45 per sq. foot
1/2 s + 3/4 s +1/4 s + 4
1 1/2 s + 4
Simplify the expression by distributing and then combining like terms.
8y - 1/2(4y - 16)
6y + 8
-6x - 10 = 20
x = -5
45 = -9(-p + 6)
p = 11
During a film festival, the first film ticket is priced at $16, and each additional ticket is $11. If Rico spends $71, then how many additional film tickets did he purchase?
Equation: 16 + 11x = 71
Answer: Rico purchased 5 additional film tickets.
7.8c + 6p – 3.4c – 10
4.4c + 6p - 10
Mr. Glass asked his students to write an expression that was equivalent to -5(4x - 9). Show which students completed the task correctly.
Lang: -10(2x - 4) + 5
Caitlyn: -20x + 45
Ezra: 3(7x - 15) - x
Clarita: 5 - 20(x - 2)
Land, Caitlyn, & Clarita
10 = -9 - x
x = -19
28 – 2(5a – 3) = 47
a = -1.3
Five sisters each bought matching scarves and two pairs of socks. The scarves were priced at $12.00. If the total bill for all 5 sisters was $125.00, what was the price of one pair of socks?
Equation: 5(2x + 12) = 125
Answer: A pair of socks cost $6.50.
8k + 4 – 11k + 9
-3k + 13
Simplify each expression using the distributive property.
a. 2.5(r - 1)
b. -8(3f - 9)
c. (t + p)4
a. 2.5r - 2.5
b. -24f + 72
c. 4t + 4p
3.2x + 12 = 48
x = 11.25
6m + 4(-2m + 6) = 10
m = 7
Asher’s sister is eight years older than Asher. Their combined ages add up to 20. How old is Asher?
Equation: (a + 8) + a = 20
Answer: Asher is 6.
Write an expression to represent the perimeter of the figure below.
Side length: x + 2
Width: 2x - 3
6x - 2
Factor each expression by dividing out the GCF.
a. 2x + 2y
b. -6b - 15
c. 10c - 25
a. 2(x + y)
b. -3(2b + 5)
c. 5(2c - 5)
Solve both:
a. 2/3x - 6 = 10
b. x/4 + 5 = 25
a. x = 24
b. x = 80
Solve both:
a. 1/2(6g + 2) = 12
b. 17 + r/3 = 28
a. g = 3.6666666666666 or 3 2/3
b. r = 33
On Halloween night, Mack collects x pieces of candy and then eats 7 pieces. The next day he eats 10% of his candy pieces and has 63 pieces remaining. How many pieces of candy did he collect on Halloween night?
Equation: 0.90(x - 7) = 63
Answer: He collected 77 pieces of candy .