Here are a few examples of linear equations with their solutions:

Example 1:

Equation:
$2x + 3 = 7$

Solution:

1. Subtract 3 from both sides:
   $2x = 7 - 3$
   $2x = 4$
2. Divide both sides by 2:
   $x = \frac{4}{2}$
   $x = 2$

Answer:
$x = 2$

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Example 2:

Equation:
$5x - 4 = 11$

Solution:

1. Add 4 to both sides:
   $5x = 11 + 4$
   $5x = 15$
2. Divide both sides by 5:
   $x = \frac{15}{5}$
   $x = 3$

Answer:
$x = 3$

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Example 3:

Equation:
$3x + 5 = 2x + 9$

Solution:

1. Subtract $2x$ from both sides:
   $3x - 2x + 5 = 9$
   $x + 5 = 9$
2. Subtract 5 from both sides:
   $x = 9 - 5$
   $x = 4$

Answer:
$x = 4$

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Example 4:

Equation:
$4(x - 2) = 3x + 5$

Solution:

1. Expand both sides:
   $4x - 8 = 3x + 5$
2. Subtract $3x$ from both sides:
   $4x - 3x - 8 = 5$
   $x - 8 = 5$
3. Add 8 to both sides:
   $x = 5 + 8$
   $x = 13$

Answer:
$x = 13$

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Example 5:

Equation:
$7x + 2 = 5x + 14$

Solution:

1. Subtract $5x$ from both sides:
   $7x - 5x + 2 = 14$
   $2x + 2 = 14$
2. Subtract 2 from both sides:
   $2x = 14 - 2$
   $2x = 12$
3. Divide both sides by 2:
   $x = \frac{12}{2}$
   $x = 6$

Answer:
$x = 6$

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If you would like a deeper explanation or have any questions about the steps, feel free to ask!

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Related Questions:

1. How do you solve an equation with fractions?
2. What are systems of linear equations and how do you solve them?
3. How do you graph a linear equation?
4. What is the difference between a linear equation and a quadratic equation?
5. How do you check if a solution to a linear equation is correct?

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Tip: Always isolate the variable step by step, performing inverse operations in reverse order (like addition/subtraction first, then multiplication/division). This method will keep your work organized.