Here are some examples of one-variable equations solved using the "looking inside" method. The method involves isolating the variable step by step by looking at the operations applied to it and reversing them.

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Example 1

Equation:
$3x + 5 = 20$

Solution:

1. Start by "looking inside" and undo the outermost operation: Subtract 5 from both sides:
   $3x = 15$
2. Now divide both sides by 3 to isolate $x$:
   $x = 5$

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Example 2

Equation:
$\frac{x - 4}{2} = 6$

Solution:

1. Undo the division by 2 by multiplying both sides by 2:
   $x - 4 = 12$
2. Add 4 to both sides to isolate $x$:
   $x = 16$

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Example 3

Equation:
$5(x + 3) = 25$

Solution:

1. Divide both sides by 5 to simplify:
   $x + 3 = 5$
2. Subtract 3 from both sides:
   $x = 2$

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Example 4

Equation:
$2(x - 7) + 3 = 13$

Solution:

1. Subtract 3 from both sides:
   $2(x - 7) = 10$
2. Divide by 2 to simplify:
   $x - 7 = 5$
3. Add 7 to both sides:
   $x = 12$

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Example 5

Equation:
$4x - 6 = 10$

Solution:

1. Add 6 to both sides:
   $4x = 16$
2. Divide by 4:
   $x = 4$

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Would you like a deeper explanation of any step or method?

Relative Questions

1. Can you explain why we reverse operations when solving equations?
2. How do we handle equations involving fractions on both sides?
3. What changes when solving equations with variables on both sides?
4. Could you demonstrate a real-world example using this method?
5. What if there are multiple steps to undo—how do we decide where to start?

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