Vocab
a symbol (usually a letter) standing in for an unknown numerical value
variable
6(x + 3) = 48
x = 5
–0.6(x + 9) = –18
x = 21
Anthony cooks 6 servings of a meal containing
pasta and meat. Each serving has 3 ounces of
meat and an equal amount of pasta. The
recipe makes a total of 42 ounces. Determine
how many ounces of pasta are in one serving.
6(3 + p) = 42; 4 oz
Inez has 6 glasses of water. After a week,
2 ounces of water evaporate from each glass.
Afterward, the glasses contain a total of 30
ounces of water. Determine the original
volume of water in each glass.
6(w – 2) = 30; 7 oz
a number sentence stating that two quantities are equal.
equation
–5(x + 2) = –70
x = 12
0.25(x – 16) = 21
x = 100
Tamara makes 12 identical flower
arrangements, each with 3 roses and an equal
number of carnations. She uses a total of
96 flowers. Determine how many carnations
are in each arrangement.
12(3 + c) = 96; 5 carnations
Melinda has 4 boxes of colored pens. After
she gives 8 pens from each box to her friends
at school, the total number of pens she has
left is 32. Determine the original number of
pens in each box.
4(t– 8) = 32; 16 pens
the value of a variable that makes an equation true.
solution
9(x + 8) = 18
x = –6
5/9(x + 28) = 25
x = 17
Francisco makes 4 identical bags of trail mix.
Each bag has 2.5 ounces of peanuts and an
equal weight of raisins. He uses 16 ounces
altogether. Determine how many ounces of
raisins are in one bag.
4(2.5 +r) = 16, r=1.5 oz.
Pete buys 5 identical boxes of golf balls. After
he removes 2 golf balls from each box, the
total number of golf balls in the boxes is 15.
Determine the original number of golf balls in
each box.
5(b – 2) = 15; 5 golf balls
Lets you multiply a sum by multiplying each addend separately and then add the products.
Distributive Property
2(x + 5) = –24
x = –17
-2/3(x − 13) = 24
x = –23
Robin prints 10 similar wall art designs. Each
design has 5 red circles and an equal number
of blue circles. She prints 90 circles in all.
Determine how many blue circles are in one
design.
10(5 + b) = 90; 4 blue circles
Amy and her friend earn equivalent
paychecks after working eight hours. They
each spend $40 of their paycheck. Afterward,
the total amount of money they have is $90.
Determine the original amount of Amy’s
paycheck.
2(p – 40) = 90; $85
if both sides of an equation are divided by a common real number that is not equal to 0, the quotients remain equal.
Division Property of Equality
–5(x + 3) = –95
x = 16
1/4(x + 7) = 8
x = 25
Terrance works out each day for 7 consecutive
days by running and walking. His workout is
identical each day. First he runs 5 miles, and
then he walks a distance. His total distance
over 7 days is 49 miles. Determine how far
Terrance walks each day.
7(5 + w) = 49; 2 miles
Gustavo serves 6 identical plates of fruit to
his friends. They each eat 4 pieces of fruit.
Afterward, 48 pieces of fruit are left.
Determine how many pieces of fruit were
originally on each plate.
6(f – 4) = 48; 12 pieces of fruit