To solve the given equation for [tex]\( y \)[/tex]:
[tex]\[ q \cdot (a + y) = 67y + 93 \][/tex]
we will follow these steps:
### Step 1: Expand the Equation
First, distribute [tex]\( q \)[/tex] on the left-hand side of the equation:
[tex]\[ q \cdot a + q \cdot y = 67y + 93 \][/tex]
### Step 2: Collect Like Terms
Next, we need to collect all terms involving [tex]\( y \)[/tex] on one side of the equation and the constants on the other side. To do this, we can subtract [tex]\( q \cdot y \)[/tex] from both sides:
[tex]\[ q \cdot a = 67y + 93 - q \cdot y \][/tex]
Combine the [tex]\( y \)[/tex] terms on the right-hand side:
[tex]\[ q \cdot a = y \cdot (67 - q) + 93 \][/tex]
### Step 3: Isolate [tex]\( y \)[/tex]
To isolate [tex]\( y \)[/tex], subtract 93 from both sides:
[tex]\[ q \cdot a - 93 = y \cdot (67 - q) \][/tex]
Now, divide both sides by [tex]\( (67 - q) \)[/tex] to solve for [tex]\( y \)[/tex]:
[tex]\[ y = \frac{q \cdot a - 93}{67 - q} \][/tex]
We have now isolated [tex]\( y \)[/tex] and thus found the solution:
[tex]\[ y = \frac{-a \cdot q + 93}{67 - q} \][/tex]
This gives the solution for [tex]\( y \)[/tex] as:
[tex]\[ y = \frac{-a \cdot q + 93}{67 - q} \][/tex]
