Academic Worksheet 3.1
Tell whether the given value of the variable is a solution of the equation.
1. 1 = 4𝑥 + 9; 𝑥 = −2
2. 8 − 3𝑥 = 5; 𝑥 = −1
Solve the equation. Check your solution.
3. 7𝑥 + 12 = 26
4. 2𝑥 + 9 = −5
6. 25 − 3𝑥 = −8
9.
𝑥
12
+ 13 = 18
7. 70 = 19 − 3𝑥
𝑥
10. 10 = 8 − 7
5. −10 = 6𝑥 − 16
8. −2𝑥 − 47 = −11
11. 
x
 12  23
9
Write the verbal sentence as an equation. Then solve the equation.
12. Negative sixteen plus the quotient of a number and 2 is 35.
13. Fourteen minus the product of 3 and a number is 26.
14. You are buying a digital camera that costs $375. The store lets you make a down payment. You can
pay the remaining cost in four equal monthly payments with no interest charged. You make a down
payment of $175. Which equation can you use to find the amount of each monthly payment?
A. 375 = 175 + 4𝑝
B. 375 = 4𝑝 − 175
C. 375 + 4𝑝 = 175
15. Use the information from Exercise 14 to find the amount of each monthly payment.
16. For one day, a barber has 28 customers and receives $64 in tips. The barber charges a flat rate for
haircuts and makes a total of $456 including tips. Which equation can you use to find how much the
barber charges for a haircut?
A. 28𝑥 − 456 = 64
B. 28𝑥 − 64 = 456
C. 28𝑥 + 64 = 456
17. Use the information from Exercise 16 to find how much the barber charges for a haircut.
Academic Worksheet 3.2 – Day 1
Tell whether the given value of the variable is a solution of the equation.
1. 5 + 𝑥 + 3 = 14; 𝑥 = 7
2. 4(𝑥 + 7) = 16; 𝑥 = −3
Solve the equation. Check your solution.
3. 3𝑥 + 8 + 𝑥 = 28
4. 9𝑥 + 7 − 2𝑥 = 14
5. 17 + 3𝑥 − 11 = 0
6. 12𝑥 − 1 − 10𝑥 = 23
7. 3(6 − 𝑥) = 27
8. −2(𝑥 + 7) = 16
9. −40 = 4(𝑥 − 10)
10. 20 = −5(𝑥 + 7)
11. −6(2𝑥 + 3) = 42
Find the value of 𝑥 for the given triangle, rectangle, or square.
12. Perimeter = 30 units
13. Perimeter = 20 units
14. You spend $91 shopping for new clothes. You spend $24 for a pair of jeans and $35 for a pair of shoes.
You also buy 4 shirts that cost 𝑑 dollars. How much is each shirt?
Academic Worksheet 3.2 – Day 2
Tell whether the given value of the variable is a solution of the equation.
1. 18 − 2(𝑥 − 3) = 26; 𝑥 = 1
Solve the equation. Check your solution.
3. 12(4 − 3𝑔) = −132
2. −2(7 − 11𝑣) = 96
4. −5(𝑐 − 1) = −55
5. 10𝑎 + 5(2𝑎 + 1) = 65
6. 18𝑏 + 8(3𝑏 + 7) = 98
7. 13 − (𝑥 + 7) = 29
8. 11𝑧 − 3(𝑧 − 9) = 123
9. 10 + 3(𝑥 + 2) = 31
10. 12(𝑥 + 3) − 3𝑥 = 117
Find the value of 𝑥 for the given triangle, rectangle, or square.
11. Perimeter = 24 units
12. Perimeter = 52 units
13. You spend $55 shopping for birthday gifts. You buy one of your friends a gift certificate for $15, and
your other friend a pair of shorts for $16. You also buy your older brother 2 compact discs that each
cost 𝑑 dollars. How much is each compact disc? Write and solve an equation.
14. The perimeter of a rectangular picture frame is 30 inches. The length of the frame is three less than
twice the width. What are the dimensions of the frame? Write and solve an equation.
Academic Worksheet 3.3
1.
Tell whether 𝑥 = −7 is a solution of the equation −3𝑥 − 13 = −7𝑥 + 15.
Solve the equation. Check your solution.
2. 9𝑥 = 7𝑥 + 22
3. 11 − 2𝑥 = 31 − 7𝑥
4. 3(4𝑥 − 1) = 12𝑥
5. 3(−2𝑥 + 5) = 11 − 4𝑥
6. −6(4𝑥 + 3) = 6(−4𝑥 − 3)
7. −3(8𝑥 + 11) = 6(−4𝑥 − 13)
Write the verbal sentence as an equation. Then solve the equation.
8. Negative thirteen times a number plus 20 is equal to -11 times the number plus 38.
9. Twenty nine less than -10 times a number is equal to -18 times the number plus 91.
Find the perimeter of the square.
10.
11.
12. You and your brother are saving money to buy a camcorder. You already have $60 saved and your
brother has $45 saved. You plan on saving an additional $5 each week. Your brother plans on saving
an additional $8 each week. Write and solve an equation to find how many weeks it takes both of you
to save the same amount. Let 𝑤 represent the number of weeks.
13. The length of a football field including the end zones is 48 feet longer than four times the length of a
tennis court. It is also 282 feet longer than a tennis court. Write and solve an equation to find the
length (in feet) of a tennis court and a football field. Let 𝑡 represent the length of a tennis court.