To solve for \( k \) in the equation \( x = 4 - \frac{k}{6} \), follow these steps:

### Step 1: Start with the given equation
\[
x = 4 - \frac{k}{6}
\]

### Step 2: Isolate the term involving \( k \)
Subtract 4 from both sides:
\[
x - 4 = -\frac{k}{6}
\]

### Step 3: Eliminate the negative sign
Multiply both sides by -1 to get:
\[
-(x - 4) = \frac{k}{6}
\]

### Step 4: Solve for \( k \)
Multiply both sides by 6 to isolate \( k \):
\[
k = 6 \cdot (-(x - 4)) = 6 \cdot (4 - x)
\]

Thus, the solution is:
\[
k = 24 - 6x
\]

Would you like more details or have any questions?

Here are 5 related questions to further explore:
1. What if \( x \) were a fraction? How would that change the solution for \( k \)?
2. How would you check if the value of \( k \) is correct for a specific \( x \)?
3. How does this equation change if \( k \) has a coefficient other than 6?
4. Can you graph the relationship between \( k \) and \( x \)?
5. What happens if \( k \) appears in the denominator more than once?

**Tip:** Always keep track of the signs during algebraic manipulations to avoid mistakes in the final solution.

Explore how to solve the linear equation x = 4 - k/6 for k with step-by-step guidance. This problem illustrates algebraic concepts like isolating variables and solving for unknowns. Ideal for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation