Math 6/7
Equations Study Guide
SOLs 6.18 & 7.14a, b
Summative Assessment Date: _______________________________________________________
What do I need to know for the upcoming assessment?

How to solve single- and two-step linear equations with one variable including operations
with:
o Integers;
o Fractions and mixed numbers; and
o Decimals

Translate equations and solve.

How to solve practical (word) problems using single- and two-step linear equations.
Will I be able to use a calculator during the assessment?
Yes, calculators will be provided for this assessment; however, you must be able to show
your work to earn full credit for your answers.
What should I do to prepare for the assessment?



Complete the attached practice problems;
Complete and review all notes and classwork; and
ASK for help before the assessment
Is there IXL practice that I can use to help me prepare and get a better grade?
YES! See below.
Grade
7th
7th
7th
6th
6th
6th
Strand
S.5
S.6
S.7
Z.6
Z.9
Z.11
SG-M67-Equations 2016-2017
Description
Solve one-step equations
Solve two-step equations
Solve equations – word problems
Solve one- step equations with fractions and mixed numbers
Solve two-step equations
Solve equations with integers
Equations Practice Problems
Directions: Solve and check each linear equation using additive and multiplicative inverses. All
fraction and answers must be a proper fraction in simplest form. Do not provide
decimal answers for fraction problems. SHOW ALL WORK.
7
3
1)
𝑛 − (−3) = −5
2)
38 = 𝑚 − 44
3)
𝑏 + 2.3 = 1.6
4)
−18 = 𝑢 − (−43)
5)
𝑓
= −5
25
6)
− 3 𝑧 = 22
7)
5
𝑑 = −15
8)
5
9)
−2𝑔 = 14
10)
−12 = 7𝑤
11)
−36 = 0.9𝑣
12)
−4𝑥 = 27
13)
1
14)
8 − (−3𝑥) = −19
6
3
𝑥 + 2 = 11
SG-M67-Equations 2016-2017
2
9
2
= 3ℎ
15)
2𝑥 + 1 = −11
16)
𝑔+19
17)
−32 = −4 + 7𝑥
18)
−12 =
19)
60 = −3(−2𝑦 + 6)
20)
4 (−𝑥 − 4) = −13
21)
– (7 − 𝑥) = −19
22)
7
23)
𝑑−(−8)
24)
−9 =
25)
The sum of five and twice a number is
fifteen. What is the number?
26)
Negative five times the sum of a
number and seven is negative twelve.
27)
Negative six is the same as nine less
than a number.
28)
Allison has $59 to spend on eight
shirts. After buying them she had $3
left. How much did each shirt cost?
−4
= −13
SG-M67-Equations 2016-2017
−3
= −21
−3
𝑥
3
𝑚
= −5
14−𝑚
−2
29)
Carlos is building a screen door. The
height of the door is 1 foot more than
twice its width. What is the width of
the door if it is 7 feet high?
30)
Brandon earns money by making
copies. He gets paid $7.00 for the first
hour and $8.00 for each additional
hour. Write an equation and
determine how much money he will
1
earn for working 6 4 hours.
31)
Ella swims four times a week at her
club’s pool. She swims the same
number of laps on Monday,
Wednesday, and Friday, and 15 laps
on Saturday. She swims a total of 51
laps each week. How many laps does
she swim on Monday?
32)
While at the music store, Drew bought
5 CDs, all at the same price. The tax on
his purchase was $6, and the total was
$61. What was the price of each CD?
33)
At the market, Meyer buys a bunch of
bananas for $0.35 per pound and a
frozen pizza for $4.99. The total for
his purchase was $6.04, without tax.
How many pounds of bananas did
Meyer buy?
34)
Morgan works at a restaurant and
earns $9.75 per hour. She puts one
third of her money into savings. How
many hours will she need to work to
save $195?
35)
Over the weekend, Koko spent 2
hours on an assignment, and she
spent equal amounts of time studying
for 4 exams for a total of 16 hours.
How much time did she spend
studying for each exam?
36)
Steve is eighteen less than twice
Lynn’s age. If Steve is 28 how old is
Lynn?
37) Identify (circle) the equations with the equivalent values for the variable x.
𝑥 + 5 = 11
SG-M67-Equations 2016-2017
𝑥+3=3
𝑥
=3
2
4𝑥 = 24
Answer Key
1
1)
𝑛 = −8
2)
𝑚 = 88
21) 𝑥 = −12
3)
𝑏 = −0.7
22) 𝑚 = −1 5
4)
𝑢 = −61
23) 𝑑 = 44
5)
𝑓 = −125
24) 𝑚 = −4
6)
𝑧 = −33
25) 5 + 2𝑥 = 15
7)
𝑑 = −18
8)
ℎ=6
27) −6 = 𝑛 − 9
9)
𝑔 = −7
28) $7
20) 𝑥 = 2 2
5
2
𝑥=5
26) −5(𝑛 + 7) = −12
5
5
3
𝑛 = −4 5
𝑛=3
10) 𝑤 = −1 7
29) 3 ft
11) 𝑣 = −40
30) 7 + 8(ℎ − 1); Brandon earned $49
12) 𝑥 = −6
3
4
13) 𝑥 = 27
14) 𝑥 = −9
15) 𝑥 = −6
31) 12 laps
32) $11
33) 3 lbs
34) 60 hours
1
16) 𝑔 = 44
35) 3 2 hours
17) 𝑥 = −4
36) 23 years old
18) 𝑥 =
1
4
19) 𝑦 = 13
SG-M67-Equations 2016-2017
37) Boxes 1, 3, & 4