Let's solve the equation \( x = 180 - (180 - 4x) - 120 \).

### Step 1: Simplify inside the parentheses
First, simplify the expression inside the parentheses:
\[
180 - 4x
\]
So the equation becomes:
\[
x = 180 - (180 - 4x) - 120
\]

### Step 2: Distribute the negative sign
Next, distribute the negative sign to the terms inside the parentheses:
\[
x = 180 - 180 + 4x - 120
\]

### Step 3: Simplify the expression
Now, simplify the constants:
\[
180 - 180 = 0
\]
So the equation simplifies to:
\[
x = 4x - 120
\]

### Step 4: Isolate the variable \( x \)
To isolate \( x \), subtract \( 4x \) from both sides of the equation:
\[
x - 4x = -120
\]
This simplifies to:
\[
-3x = -120
\]

### Step 5: Solve for \( x \)
Finally, divide both sides by \(-3\) to solve for \( x \):
\[
x = \frac{-120}{-3} = 40
\]

So, the solution is \( x = 40 \).

If you have any questions or want more details, feel free to ask!

Here are 8 related questions:
1. How would the equation change if the constant \(120\) was increased?
2. What is the value of \( x \) if the equation was \( x = 180 - (180 - 5x) - 120 \)?
3. How do you check if your solution for \( x \) is correct?
4. What happens if you set \( x = 0 \) in the original equation?
5. How do you solve the equation if the expression inside the parentheses is \( (180 + 4x) \)?
6. What if the equation was \( x = 180 - (180 - 4x + 50) - 120 \)?
7. How can you represent this equation graphically?
8. What is the general approach to solving equations of this form?

**Tip:** Always simplify the equation step by step, starting with parentheses and combining like terms before isolating the variable.

Learn how to solve the equation x = 180 - (180 - 4x) - 120 step-by-step. This problem involves simplifying expressions and isolating variables, suitable for Grades 7-9 mathematics.

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