Question

Develop and algorithm for a two step equation

Answer 1

Certainly! A two-step equation typically looks like \( ax + b = c \), where \( a \), \( b \), and \( c \) are constants and \( x \) is the variable we want to solve for. Here's a step-by-step algorithm to solve such an equation:

### Algorithm to Solve a Two-Step Equation

1. **Identify the equation**: Start with the general form of the equation \( ax + b = c \).

2. **Reorganize the equation** (if necessary): Ensure the equation is in standard form (i.e., all terms are on one side, ideally \( ax + b - c = 0 \), or leave it as \( ax + b = c \)).

3. **Isolate the variable term**:
- Subtract \( b \) from both sides of the equation. This results in:
\[
ax = c - b
\]

4. **Solve for the variable**:
- Divide both sides of the equation by \( a \) (assuming \( a \neq 0 \)):
\[
x = \frac{c - b}{a}
\]

5. **Check your solution**:
- Substitute \( x \) back into the original equation to verify that both sides are equal.

6. **Present the solution**: Provide the value of \( x \) as the solution to the equation.

### Example

Let’s see how the algorithm works with a specific example:

#### Equation:
\[ 3x + 5 = 20 \]

#### Step-by-Step Solution Using the Algorithm

1. **Identify the equation**: \( 3x + 5 = 20 \).

2. **Reorganize the equation**: Already in standard form.

3. **Isolate the variable term**:
- Subtract 5 from both sides:
\[
3x = 20 - 5 \implies 3x = 15
\]

4. **Solve for the variable**:
- Divide both sides by 3:
\[
x = \frac{15}{3} \implies x = 5
\]

5. **Check your solution**:
- Substitute \( x = 5 \) back into the original equation:
\[
3(5) + 5 = 15 + 5 = 20 \quad \text{(True)}
\]

6. **Present the solution**: The solution is \( x = 5 \).

This algorithm can be applied to any two-step equation by following these steps to isolate the variable and solve for it.