Use this visual guide to walk students through the five essential steps of solving multi-step algebraic equations.

The image provides a step-by-step guide for solving equations, along with an example problem. Let's break it down and solve the equation step by step.

Steps for Solving Equations

1. Distribute on each side of the equation.
2. Combine like terms on each side of the equation.
3. Move the variable to one side of the equation.
4. Undo addition/subtraction.
5. Undo multiplication/division.

Example Problem

Solve for \( x \):
\[
3(2x + 1) - x = 3x + 7
\]

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Step-by-Step Solution

#### Step 1: Distribute
First, distribute the \( 3 \) across the terms inside the parentheses on the left-hand side:
\[
3(2x + 1) - x = 3x + 7
\]
\[
3 \cdot 2x + 3 \cdot 1 - x = 3x + 7
\]
\[
6x + 3 - x = 3x + 7
\]

#### Step 2: Combine Like Terms
Combine the \( x \)-terms on the left-hand side:
\[
6x - x + 3 = 3x + 7
\]
\[
5x + 3 = 3x + 7
\]

#### Step 3: Move the Variable to One Side
To isolate \( x \), subtract \( 3x \) from both sides of the equation:
\[
5x + 3 - 3x = 3x + 7 - 3x
\]
\[
2x + 3 = 7
\]

#### Step 4: Undo Addition/Subtraction
Subtract 3 from both sides to isolate the term with \( x \):
\[
2x + 3 - 3 = 7 - 3
\]
\[
2x = 4
\]

#### Step 5: Undo Multiplication/Division
Divide both sides by 2 to solve for \( x \):
\[
\frac{2x}{2} = \frac{4}{2}
\]
\[
x = 2
\]

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Final Answer

\[
\boxed{x = 2}
\]

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Explanation

1. Distribution: We expanded the expression \( 3(2x + 1) \) to simplify the equation.
2. Combining Like Terms: We combined \( 6x \) and \( -x \) to get \( 5x \).
3. Moving Variables: We moved all \( x \)-terms to one side by subtracting \( 3x \) from both sides.
4. Undoing Addition: We isolated the term with \( x \) by subtracting 3 from both sides.
5. Undoing Multiplication: Finally, we divided both sides by 2 to solve for \( x \).

This method ensures that the equation is solved systematically and accurately.