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
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Identify the equation: Start with the general form of the equation \( ax + b = c \).
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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 \( ax + b = c \)).
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Isolate the variable term:
- Subtract \( b \) from both sides of the equation. This results in: \[ ax = c - b \]
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Solve for the variable:
- Divide both sides of the equation by \( a \) (assuming \( a \neq 0 \)): \[ x = \frac{c - b}{a} \]
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Check your solution:
- Substitute \( x \) back into the original equation to verify that both sides are equal.
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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
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Identify the equation: \( 3x + 5 = 20 \).
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Reorganize the equation: Already in standard form.
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Isolate the variable term:
- Subtract 5 from both sides: \[ 3x = 20 - 5 \implies 3x = 15 \]
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Solve for the variable:
- Divide both sides by 3: \[ x = \frac{15}{3} \implies x = 5 \]
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Check your solution:
- Substitute \( x = 5 \) back into the original equation: \[ 3(5) + 5 = 15 + 5 = 20 \quad \text{(True)} \]
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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.
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