One- & Two-Step Equations Review

Answer 1

Sure! Here’s a quick review of one-step and two-step equations, including their definitions, examples, and methods for solving them.

One-Step Equations

Definition: A one-step equation is an algebraic equation that can be solved in a single step by performing the inverse operation.

Common Forms:

1. \( x + a = b \)
2. \( x - a = b \)
3. \( ax = b \)
4. \( \frac{x}{a} = b \)

Examples:

1. \( x + 5 = 12 \)

   • Solution: Subtract 5 from both sides: \[ x = 12 - 5 \ x = 7 \]

2. \( x - 3 = 10 \)

   • Solution: Add 3 to both sides: \[ x = 10 + 3 \ x = 13 \]

3. \( 3x = 15 \)

   • Solution: Divide both sides by 3: \[ x = \frac{15}{3} \ x = 5 \]

4. \( \frac{x}{4} = 2 \)

   • Solution: Multiply both sides by 4: \[ x = 2 \times 4 \ x = 8 \]

Two-Step Equations

Definition: A two-step equation requires two operations to isolate the variable.

Common Forms:

1. \( ax + b = c \)
2. \( ax - b = c \)
3. \( \frac{x}{a} + b = c \)
4. \( \frac{x}{a} - b = c \)

Examples:

1. \( 2x + 3 = 11 \)

   • Solution Steps:
     1. Subtract 3 from both sides: \[ 2x = 11 - 3 \ 2x = 8 \]
     2. Divide by 2: \[ x = \frac{8}{2} \ x = 4 \]

2. \( 5x - 4 = 21 \)

   • Solution Steps:
     1. Add 4 to both sides: \[ 5x = 21 + 4 \ 5x = 25 \]
     2. Divide by 5: \[ x = \frac{25}{5} \ x = 5 \]

3. \( \frac{x}{3} + 2 = 7 \)

   • Solution Steps:
     1. Subtract 2 from both sides: \[ \frac{x}{3} = 7 - 2 \ \frac{x}{3} = 5 \]
     2. Multiply both sides by 3: \[ x = 5 \times 3 \ x = 15 \]

4. \( \frac{x}{2} - 1 = 4 \)

   • Solution Steps:
     1. Add 1 to both sides: \[ \frac{x}{2} = 4 + 1 \ \frac{x}{2} = 5 \]
     2. Multiply both sides by 2: \[ x = 5 \times 2 \ x = 10 \]

Summary

• One-step equations require one operation to isolate the variable.
• Two-step equations require two operations to isolate the variable.
• Always perform the inverse operation to solve for \( x \).

Feel free to ask for more examples or explanations on any specific topic!