Question

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!