Question

solve for x.
assume the equation has a solution for x.

d·(-3 + x) = kx + 9

x =

Explanation:

Step1: Distribute d

First, we distribute the \( d \) on the left side of the equation \( d \cdot (-3 + x) = kx + 9 \). Using the distributive property \( a(b + c)=ab + ac \), we get:
\( -3d + dx = kx + 9 \)

Step2: Collect x terms

Next, we want to get all terms with \( x \) on one side. Subtract \( kx \) from both sides and add \( 3d \) to both sides:
\( dx - kx = 9 + 3d \)

Step3: Factor x

Factor out \( x \) from the left side. Using the distributive property in reverse \( ab - ac = a(b - c) \), we have:
\( x(d - k) = 9 + 3d \)

Step4: Solve for x

Finally, divide both sides by \( (d - k) \) (assuming \( d
eq k \), but the problem states there is a solution, so we can do this):
\( x=\frac{9 + 3d}{d - k} \) or we can factor the numerator: \( x=\frac{3d + 9}{d - k}=\frac{3(d + 3)}{d - k} \)

Answer:

\( \frac{3d + 9}{d - k} \) (or \( \frac{3(d + 3)}{d - k} \))