Assume the equation has a solution for [tex] x [/tex]:

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

Solve for [tex] x [/tex].



Answer :

Certainly! Let's solve the given equation step-by-step. The given equation is:

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

To solve for \( x \), let’s go through the following steps:

### Step 1: Distribute \( d \) on the left side
First, we need to apply the distributive property to the left-hand side of the equation:

[tex]\[ d \cdot (-3 + x) = d \cdot (-3) + d \cdot x \][/tex]

So the equation becomes:

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

### Step 2: Isolate the terms involving \( x \) on one side
To isolate the term \( x \), we will rearrange the equation to combine all \( x \)-terms on one side. Let’s subtract \( kx \) from both sides:

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

### Step 3: Combine like terms
Now, we need to factor \( x \) on the left-hand side:

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

### Step 4: Solve for \( x \)
Next, let's isolate \( x \) by dividing both sides of the equation by the factor \((d - k)\):

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

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

So the solution for \( x \) is:

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

This is the value of [tex]\( x \)[/tex] that satisfies the given equation [tex]\( d \cdot (-3 + x) = k \cdot x + 9 \)[/tex].