Academic Worksheet 2.4
Write the verbal sentence as an equation.
1. The difference of 11 and 𝑦 is -9.
3.
2.
The quotient of 𝑟 and 6 is -4.
The sum of 41 and 𝑤 is 26.
4. The product of 18 and 𝑝 is 54.
Tell whether the given value of the variable is a solution of the equation.
5. 108 = −36𝑧; 𝑧 = −3
6. 27 = 𝑛 − 16; 𝑛 = 11
7. 84 = 78 + 𝑡; 𝑡 = −6
Match the equation with the corresponding question.
𝑎
A. What number minus 36 equals 2?
8.
= 36
2
9. 2𝑎 = 36
B.
10. 2 + 𝑎 = 36
C. 2 times what number equals 36?
11. 𝑎 − 36 = 2
D. 2 plus what number equals 36?
Solve the equation using mental math.
12. 12𝑏 = −108
15.
48
ℎ
= −16
18. −19 + 𝑐 = 28
What number divided by 2 equals 36?
𝑤
−3
13. 96 = −8𝑚
14.
16. 39 − 𝑓 = 15
17. 58 = 27 − 𝑙
= 21
19. 𝑔 + 26 = −61
20. While traveling a long distance, an elephant in a family walks at a rate of about 10 miles per hour.
Find the approximate time it take an elephant to travel 60 miles. Write an equation and solve using
mental math.
21. From 2003 to 2004, the number of students in a school declined by 140 students. In 2004, there were
530 students in the school. Find the number of students in the school in 2003. Write an equation and
solve using mental math.
22. The perimeter of the figure is 48 centimeters.
a. Write and simplify an equation that you can use to find 𝑥.
b. Solve your equation. What is the value of 𝑥?
Academic Worksheet 2.5
Solve the equation. Check your solution.
1. 𝑧 + 16 = 4
2.
3. −3 = 𝑗 + 5
0 = 𝑚 + 17
4. −7 + 𝑑 = −26
5. 𝑎 − 20 = −3
6. 𝑡 − 19 = 23
7. −8 + 𝑏 = −5
8. −15 = 𝑛 − 22
9. −28 + 𝑝 = −3
In Exercises 10 – 12, write an equation to model the situation. Then solve the equation.
10. Your friend is 3 years older than you. You are 15 years old. How old is your friend?
11. You pay $1.70 for a box of oatmeal after using a coupon for $0.80 off. Find the regular price of the
oatmeal.
12. There are 160 players in a soccer league. This is 23 more than last year. Find the number of players
that were in the soccer league last year.
Solve the equation. Check your solution.
13. 10 + 𝑘 + 6 = 22
14. 18 + 𝑤 − 13 = −20
Find the value of 𝑥 for the given triangle.
16. Perimeter = 70 in.
15. −5 − 11 − ℎ = −7
17. Perimeter = 37 ft.
Academic Worksheet 2.6
Solve the equation. Check your solution.
1. −6𝑦 = −84
2. 418 = 19𝑎
4.
d
 11
9
7. 9𝑚 − 6𝑚 = 21
5.
22 
g
 32
8. 144 = −8(2𝑥)
3. 126 = −21𝑝
w
 12
6.
 15 
9.
b
 4
17  4
10. Sixty-four people show up for a volleyball tournament. Write and solve an equation to find how many
4-person teams can be formed.
11. A high-speed rail service connects London, England, Paris, France, and Brussels, Belgium. One of the
high-speed trains travels about 233 miles from London to Brussels at a speed of about 87 miles per
hour. How long does the trip take?
12. A salesperson starts with a full tank of gas, drives her car 363 miles and then refuels. It takes 11
gallons of gas to fill the car’s tank. How many miles per gallon did the car get?
13. The figure shown below is composed of a triangle and a rectangle.
a. Write and simplify an expression in terms of 𝑥 for the area of the figure.
b. What is the value of 𝑥 if the area of the figure is 108 square inches?
Academic Worksheet 2.7 – Day 1
Perform the indicated operation.
1. 8.5 + 9.4
2. −10.7 + 6.3
3. −11.1 + (−7.4)
4. 3.8 − 7.6
5. −1.6 − (−2.7)
6. −13.1 − 6.5
7. −0.5(3.7)
8. −3.4(−6.2)
9. −24.5 ÷ 9.8
10. 18.24 ÷ (−3.2)
11. −7.05 ÷ 4.7
12. −34.76 + 14.88
13. Simplify the expression 2.6𝑥 − 7.1𝑥.
14. You deposit a check for $236.79 into your savings account. Your account has a balance of
$319.23 after the deposit. Find the balance of your savings account before the deposit.
15. The table shows the daily low temperature in degrees Celsius for a 5-day period.
a. Find the sum of the temperatures.
b. Find the average low temperature for the 5-day period.
Academic Worksheet 2.7 – Day 2
Simplify the expression.
1. −9.87𝑥 − 18.13𝑥
2. −56.08𝑥 + 26.68𝑥
Solve the equation. Check your solution.
4. 5.3 = 𝑓 + 7.7
3. 21.3 + 𝑟 = −19.79
5. −8.3 + 𝑎 = −11.2
6. 𝑑 − 12.4 = −4.1
7. 20.3 = 𝑡 − (−3.9)
9. −4.2 = −5.6𝑘
10.  4 
v
7 .9
8. −6𝑏 = 55.2
11.  10.5 
c
 3.2
12. The total weight of 2 puppies is 15.03 pounds. One puppy weighs 9.8 pounds. How much does the
other puppy weigh?
13. At an amusement park, you spend $7.40 on lunch and $6.20 on admission. Admission, lunch, and
playing arcade games cost $19. How much did you spend on arcade games?
Find the value of 𝑥 for the given triangle or rectangle.
14. Perimeter = 22.2 cm
15. Area 20.16 in2