SOLVE LINEAR EQUATIONS IN ONE VARIABLE WORKSHEET

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

Solve for x and find the types of solution for the equations given below. :

Problem 1 :

-5x+ 3 = 2x + 10

Solution

Problem 2 :

3x - 12x = 24 - 9x

Solution

Problem 3 :

4(2x - 3) + 4 = 8x - 8

Solution

Problem 4 :

2(x + 7) = 6x + 9 - 4x

Solution

Problem 5 :

-5(3 - 4x) = -6 + 20x + 9

Solution

Problem 6 :

-8x + 3 - 2x = - 6x + 3 - 4x

Solution

Problem 7 :

10x + 3 + 10x = 13x - 3 + 7x

Solution

Problem 8 :

0.125x = 0.025 (5x + 1)

Solution

Problem 9 :

The solution of which of the following equations is neither a fraction nor an integer.

(a) 3x + 2 = 5x + 2           (b) 4x – 18 = 2

(c) 4x + 7 = x + 2            (d) 5x – 8 = x + 4

Solution

Problem 10 :

If 8x – 3 = 25 + 17x, then x is

(a) a fraction         (b) an integer

(c) a rational number      (d) cannot be solved

Solution

Problem 11 :

The solution of the equation

3x – 4 = 1 – 2x is ____.

Solution

Problem 1 :

It took Thomas 25 minutes longer to do his math homework than to do his French homework. He spent a total of 2.25 hours on both subjects. How much time did he spend on math?

Solution

Problem 2 :

Jesse earns $6 an hour babysitting for his younger brother. His mom gave him $71 last week. This included his babysitting money and his $20 allowance. How many hours did Jesse babysit?

Solution

Problem 3 :

Carol and Cathy are each saving money for a vacation. Carol started with $25 and saves $7.50 a week. Cathy started with $10 and saves $10 a week. When will they have saved the same amount?

Solution

Problem 4 :

One weekend Bill earned 3 times as much as Jim. Tom earned $5 more than Jim. In all, they earned $60. How much did each earn?

Solution

Problem 5 :

The Maxwell children have hired a caterer to provide food for an anniversary party for their parents. The caterer has quoted a price of $96 per person and is asking for an advance payment of one-fourth of the total bill. If the advance payment is $1200, how many guests are invited to the party?

Solution

Problem 6 :

Three children each contributed toward a birthday present for their mother. The oldest contributed three times as much as the youngest, while the second oldest contributed 50 cents more than the youngest. If the present costs $10.50, how much did each contribute?

Solution

Problem 7 :

At a school game, student tickets were 50 cents each and adult tickets were $1 each. If the total receipts from 900 tickets were $500, how many tickets of each kind were sold?

Solution

Problem 8 :

A salesman sold 200 pairs of slippers. Some were sold at $6 per pair and the remainder were sold at $11 per pair. Total receipts from this sale were $1600. How many pairs of slippers were sold at $6 each?

Solution