LINEAR EQUATIONS IN ONE VARIABLE WORKSHEET

Solve the equations. Write null or all where appropriate. Show fractions in simplest form.

1)  5(y + 2) = 20           Solution

2)  2(x – 4) = 2x – 8           Solution

3)  6(k + 3) = 2(4k + 5)     Solution

4)  30 – 2x = 2(3x + 3)           Solution

5)  16 = 4(n – 5) + 4             Solution

6)  7p + 9 = 4(p – 3)          Solution

7)  3(2m + 4) = 6m + 15             Solution

8)  2(4w + 7) = 3(6 + 2w)               Solution

9)  25 = 6(c + 7) - 14            Solution

10)  3(3h + h) = 2(h + 5)         Solution

11)  3(2 + n) = 10 + 2n            Solution

Solve each equation. Indicate if an equation has no solution or infinitely many solutions.

1)  2x + 4 = 9 + x      Solution

2)  5a + 5 = 5(a + 1)   Solution

3)  5a + 5 = 5(a + 2)    Solution

4)  b + 3b – 10 = 2(2b – 5)    Solution

5)  y + 5y – 6 = 3(2y – 2)      Solution

6)  -4i – 11 = 4i/2 + 7        Solution

7)  -4z + 6 = 4(-z + 2)     Solution

8)  4i + 3 = 4(i + 1)   Solution

9)  6z + z = 5z + 10    Solution

10)  2c – c = 3c - 5     Solution

11)  12n + 7 = 4n + 8n + 6     Solution

12) 12d(3 – 2) = 24    Solution

13)  4x = x + 10.5   Solution

Determine if each equation has one solution, many solutions, or no solution. If the equation has a solution, determine the solution to the equation.

1)  2x - x + 7 = x + 3 + 4               Solution

2)  -2(x + 1) = -2x + 5        Solution

3)  4x + 2x + 2 = 3x - 7        Solution

4) 2(x + 2) + 3x = 2(x + 1) + 1      Solution

5)  4(x - 1) = 1/2(x - 8)      Solution

6)  1/2(2 - 4x) + 2x = 13      Solution

7)  3x - x + 4 = 4(2x - 1)      Solution

8)  4(2x + 1) = 5x + 3x + 9      Solution

9)  10 + x = 5(1/5x + 2)      Solution

10)  8(x + 2) = 2x + 16      Solution

11)  3 + 3/2x + 4 = 4x - 5/2x      Solution

Problem 12 :

In the 2012 Olympics, Usain Bolt won the 200-meter dash with a time of 19.32 seconds. Write and solve an equation to find his average speed to the nearest hundredth of a meter per second.

Solution

Problem 1 :

Amanda rented a bike from Shawna's Bikes. They charged her $2 per hour, plus a $10 fee. Amanda paid less than $27.

a) Write an inequality to represent the situation. Be sure to define your variable.

b) Solve the inequality to find the maximum number of hours Amanda rented the bike.

Solution

Problem 2 :

You need to buy some pencils and an eraser. You can spend no more than $5. The eraser costs $1 and the pencils cost $0.25 each.

a) Write an inequality to represent the situation. Be sure to define your variable.

b) Solve the inequality to find the maximum number of pencils you can buy

Solution

Problem 3 :

Mark's Canoes rents canoes for $20 plus $35 per hour. You do not want to spend more than $150. For how many hours can you afford to rent the canoe?

a) Write an inequality to represent the situation. Be sure to define your variable.

b) Solve the inequality and answer the question.

Solution

Problem 4 :

For a field trip 18 students rode in cars and the rest filled five buses. How many students were in each bus if no more than 250 students went on the trip?

a) Write an inequality to represent the situation. Be sure to define your variable.

b) Solve the inequality and answer the question.

Solution

Problem 5 :

Charles is saving $5 each week. He earns an extra $15 by mowing his neighbor's lawn. How many weeks will he need to save in order to have at least $75?

a) Write an inequality to represent the situation. Be sure to define your variable.

b) Solve the inequality and answer the question.

Solution

Problem 6 :

Write an inequality that represents the missing dimension x. The area is less than 42 square meters.

Solution

Problem 7 :

The area is greater than or equal to 8 square feet.

Solution

Problem 8 :

The area is less than 18 square centimeters.

Solution

Problem 9 :

The area is greater than 12 square inches.

Solution

Problem 10 :

You order the hardcover book shown from a website that offers free shipping on orders of $25 or more. Write and solve an inequality that represents how much more you must spend to get free shipping.

Solution

Problem 11 :

You are riding a train. Your carry-on bag can weigh no more than 50 pounds. Your bag weighs 38 pounds.

a. Write and solve an inequality that represents how much weight you can add to your bag.

b. Can you add both a 9-pound laptop and a 5-pound pair of boots to your bag without going over the weight limit? Explain.

Solution