When 6 is subtracted from four times a number, the result is 10. Form the equation and find the solution using trial and error method.

Answer

To solve the problem step by step using the trial and error method, we will follow these steps:

### Step 1: Form the Equation
We need to translate the statement into a mathematical equation. The statement is: "When 6 is subtracted from four times a number, the result is 10."

Let the unknown number be represented by \( x \).

The equation can be formed as:
\[ 4x - 6 = 10 \]

### Step 2: Rearranging the Equation
To check our work, we can rearrange the equation to isolate \( x \):
\[ 4x = 10 + 6 \]
\[ 4x = 16 \]
\[ x = \frac{16}{4} \]
\[ x = 4 \]

However, since we are to use the trial and error method, we will try different values for \( x \).

### Step 3: Trial and Error Method
Now, we will try different integer values for \( x \) to see which one satisfies the equation.

1. **Try \( x = 1 \)**:
\[ 4(1) - 6 = 4 - 6 = -2 \] (not equal to 10)

2. **Try \( x = 2 \)**:
\[ 4(2) - 6 = 8 - 6 = 2 \] (not equal to 10)

3. **Try \( x = 3 \)**:
\[ 4(3) - 6 = 12 - 6 = 6 \] (not equal to 10)

4. **Try \( x = 4 \)**:
\[ 4(4) - 6 = 16 - 6 = 10 \] (equal to 10)

### Conclusion
After trying the values, we find that when \( x = 4 \), the equation holds true. Therefore, the solution to the problem is:
\[ x = 4 \]

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