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].
[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].
