Here are five examples of linear equations, ranging from simple to slightly more complex:

Example 1:

Equation:
$2x + 3 = 7$

Solution:

1. Subtract 3 from both sides:
   $2x = 4$
2. Divide both sides by 2:
   $x = 2$

Example 2:

Equation:
$5y - 4 = 11$

Solution:

1. Add 4 to both sides:
   $5y = 15$
2. Divide both sides by 5:
   $y = 3$

Example 3:

Equation:
$3x + 2 = 4x - 1$

Solution:

1. Subtract $3x$ from both sides:
   $2 = x - 1$
2. Add 1 to both sides:
   $x = 3$

Example 4:

Equation:
$6z - 3 = 2z + 9$

Solution:

1. Subtract $2z$ from both sides:
   $4z - 3 = 9$
2. Add 3 to both sides:
   $4z = 12$
3. Divide both sides by 4:
   $z = 3$

Example 5:

Equation:
$\frac{x}{2} + 5 = \frac{3x}{4}$

Solution:

1. Multiply the entire equation by 4 to eliminate the fractions:
   $2x + 20 = 3x$
2. Subtract $2x$ from both sides:
   $20 = x$

Would you like more details or explanations on any of these examples?

Relative Questions:

1. How can you identify if an equation is linear or not?
2. What are the common steps to solve linear equations with fractions?
3. How can linear equations be used in real-life problem-solving?
4. How do we solve linear equations with variables on both sides?
5. How can we apply linear equations in two variables?

Tip: Always isolate the variable on one side of the equation by performing the same operation on both sides.