**Solving Linear Equations: A Step-by-Step Guide**

Linear equations are mathematical expressions that represent a straight line when graphed. They are of the form:

\[
ax + b = c
\]

where:
- \(a\), \(b\), and \(c\) are constants (numbers),
- \(x\) is the variable we need to solve for.

### Steps to Solve a Linear Equation

#### 1. **Simplify Both Sides**
   - If the equation has parentheses, distribute to eliminate them.
   - Combine like terms on each side of the equation.

#### 2. **Isolate the Variable**
   - To get the variable (\(x\)) on one side, we need to "undo" the operations around it by performing opposite operations (addition becomes subtraction, multiplication becomes division, etc.).
   
   - Start by adding or subtracting to move any constants (\(b\) or \(c\)) to the other side.
   
   \[
   ax + b = c \quad \Rightarrow \quad ax = c - b
   \]

#### 3. **Solve for the Variable**
   - Once the variable term (\(ax\)) is isolated, solve for \(x\) by dividing by the coefficient of \(x\) (which is \(a\)).
   
   \[
   ax = d \quad \Rightarrow \quad x = \frac{d}{a}
   \]

#### 4. **Check Your Solution**
   - Substitute the value of \(x\) back into the original equation to verify that both sides are equal.

### Example Problem

Solve the equation: \(3x + 5 = 14\).

**Step 1: Simplify Both Sides**
   - The equation is already simplified.

**Step 2: Isolate the Variable**
   - Subtract 5 from both sides:
   
   \[
   3x + 5 - 5 = 14 - 5
   \]
   \[
   3x = 9
   \]

**Step 3: Solve for the Variable**
   - Divide both sides by 3:
   
   \[
   x = \frac{9}{3} = 3
   \]

**Step 4: Check Your Solution**
   - Substitute \(x = 3\) back into the original equation:
   
   \[
   3(3) + 5 = 14 \quad \text{(True!)}
   \]

### Summary
- Simplify both sides of the equation.
- Isolate the variable by moving terms around.
- Solve for the variable.
- Check your solution.

**Do you want more details on any of these steps, or do you have any questions?**

### Related Questions:
1. How do you solve a linear equation with variables on both sides?
2. What happens if a linear equation has no solution?
3. How can you solve a linear equation with fractions?
4. How do you solve a linear equation with decimals?
5. What are the properties of equality used in solving equations?

**Tip:** Always perform the same operation on both sides of the equation to maintain the equality!

Learn how to solve linear equations step-by-step with examples. Understand the fundamental algebraic concepts involved in solving equations. Suitable for Grades 7-9.

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