Introduction to One-Step Equations

Today, we’re going to learn about one-step equations. These are equations that can be solved by doing just one operation, like adding, subtracting, multiplying, or dividing.

What is an Equation?

An equation is like a balance scale. What you do to one side, you must do to the other side to keep it balanced. For example:

$$

x + 3 = 7

$$

This means, if you add 3 to some number (x), you get 7.

Solving One-Step Equations

To solve one-step equations, our goal is to find the value of (x). Here are the steps:

  1. Identify the operation: Look at what is happening to (x).
  2. Do the opposite: To isolate (x), do the opposite operation.
  3. Solve: Calculate the answer.

Examples

Example 1: Addition

Let’s solve this equation:

$$

x + 5 = 12

$$

  • Identify the operation: Here, we see that we are adding 5 to (x).
  • Do the opposite: The opposite of adding 5 is subtracting 5.
  • Solve:

$$

x = 12 – 5

$$

So,

$$

x = 7

$$

Example 2: Subtraction

Now, let’s try this one:

$$

x – 4 = 10

$$

  • Identify the operation: We are subtracting 4 from (x).
  • Do the opposite: The opposite of subtracting 4 is adding 4.
  • Solve:

$$

x = 10 + 4

$$

So,

$$

x = 14

$$

Key Rules

  1. Always do the opposite operation.
  2. What you do to one side, do to the other.
  3. Check your answer by plugging it back into the original equation.

Tips and Tricks

  • Use a number line to help understand addition and subtraction.
  • Practice regularly to get comfortable with different equations.
  • Write it down: Sometimes, writing the steps can help you remember them.

Questions

Easy Level (20 Questions)

  1. (x + 2 = 5)
  2. (x – 3 = 1)
  3. (x + 4 = 9)
  4. (x – 1 = 6)
  5. (x + 6 = 10)
  6. (x – 5 = 0)
  7. (x + 10 = 15)
  8. (x – 7 = 2)
  9. (x + 8 = 14)
  10. (x – 4 = 5)
  11. (x + 3 = 8)
  12. (x – 2 = 3)
  13. (x + 1 = 4)
  14. (x – 6 = -1)
  15. (x + 5 = 12)
  16. (x – 8 = 1)
  17. (x + 7 = 13)
  18. (x – 3 = 4)
  19. (x + 2 = 10)
  20. (x – 5 = -2)

Medium Level (20 Questions)

  1. (2 + x = 7)
  2. (15 – x = 4)
  3. (3 + x = 9)
  4. (x – 9 = -3)
  5. (x + 11 = 20)
  6. (x – 12 = 3)
  7. (x + 5 = 2x)
  8. (x – 3 = x – 8)
  9. (10 – x = 5)
  10. (x + 2 = 3x – 4)
  11. (x + 6 = 3)
  12. (4 + x = 10 – x)
  13. (x – 5 = 5 – x)
  14. (x + 9 = 18 – x)
  15. (6 + x = 2x – 2)
  16. (x – 4 = 10 – x)
  17. (x + 1 = 2x + 1)
  18. (7 – x = 4)
  19. (2 + x = 3x – 4)
  20. (x + 4 = x – 2)

Hard Level (20 Questions)

  1. (2x – 3 = 5)
  2. (3x + 6 = 15)
  3. (5 – 2x = 3)
  4. (x + 4 = 3x – 2)
  5. (x – 7 = 2x + 3)
  6. (3 + 4x = 19)
  7. (10x – 5 = 5x + 10)
  8. (15 – 3x = 0)
  9. (x + 8 = 2x + 4)
  10. (2x – 6 = 3x + 2)
  11. (x – 4 = 2x – 8)
  12. (9 + 4x = 33)
  13. (3x + 1 = x + 9)
  14. (5x – 10 = 0)
  15. (8 + x = 3x + 2)
  16. (4x – 3 = 2x + 5)
  17. (7 + 2x = 19 – x)
  18. (x – 2 = 3x – 8)
  19. (10 – x = 3x – 6)
  20. (x + 5x – 4 = 2x + 8)

Answers

Easy Level Answers

  1. (x = 3)
  2. (x = 4)
  3. (x = 5)
  4. (x = 7)
  5. (x = 4)
  6. (x = 5)
  7. (x = 5)
  8. (x = 9)
  9. (x = 6)
  10. (x = 9)
  11. (x = 5)
  12. (x = 5)
  13. (x = 3)
  14. (x = 5)
  15. (x = 7)
  16. (x = 9)
  17. (x = 6)
  18. (x = 7)
  19. (x = 8)
  20. (x = 3)

Medium Level Answers

  1. (x = 5)
  2. (x = 11)
  3. (x = 6)
  4. (x = 6)
  5. (x = 9)
  6. (x = 15)
  7. (x = 1)
  8. (x = 5)
  9. (x = 5)
  10. (x = 5)
  11. (x = -3)
  12. (x = 3)
  13. (x = 5)
  14. (x = 4)
  15. (x = 6)
  16. (x = 12)
  17. (x = 7)
  18. (x = 7)
  19. (x = 1)
  20. (x = 2)

Hard Level Answers

  1. (x = 4)
  2. (x = 3)
  3. (x = 1)
  4. (x = 3)
  5. (x = -2)
  6. (x = 3.25)
  7. (x = 3)
  8. (x = 5)
  9. (x = 2)
  10. (x = 4)
  11. (x = 4)
  12. (x = 6)
  13. (x = 4)
  14. (x = 2)
  15. (x = -3)
  16. (x = 4)
  17. (x = 4)
  18. (x = 3)
  19. (x = 4)
  20. (x = 6)

Happy solving, and remember to practice!