https://file.aiquickdraw.com/mathbot/file/1725602278404fl9vynqz.jpg

The given equation is:

\[
d \cdot (-3 + x) = kx + 9
\]

To solve for \( x \), let's proceed step by step:

### Step 1: Expand the left-hand side
Distribute the \( d \) on the left-hand side:

\[
d(-3) + d(x) = kx + 9
\]

This simplifies to:

\[
-3d + dx = kx + 9
\]

### Step 2: Group terms with \( x \)
Move all terms involving \( x \) to one side and constants to the other:

\[
dx - kx = 9 + 3d
\]

### Step 3: Factor out \( x \)
Factor \( x \) on the left-hand side:

\[
x(d - k) = 9 + 3d
\]

### Step 4: Solve for \( x \)
Now, solve for \( x \) by dividing both sides by \( d - k \):

\[
x = \frac{9 + 3d}{d - k}
\]

Thus, the solution is:

\[
x = \frac{9 + 3d}{d - k}
\]

---

Would you like further details on this, or do you have any questions?

Here are 5 related questions to consider:
1. How would the equation change if the constant 9 were replaced by another variable?
2. What happens to \( x \) if \( d = k \)?
3. Can this equation have multiple solutions, and under what conditions?
4. How would the solution for \( x \) change if there were additional terms?
5. What does the behavior of \( x \) indicate when \( d \) approaches \( k \)?

**Tip:** Always check the denominator to ensure there are no divisions by zero. For example, in this case, \( d \neq k \).

Learn how to solve the equation d(-3 + x) = kx + 9 step by step. This problem covers key algebraic concepts such as distributing, factoring, and solving linear equations. Suitable for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation