Solve for : `(4z - 7)/(3 - 2z) = -5`

Answer

To solve the equation \(\frac{4z - 7}{3 - 2z} = -5\), we will follow these steps:

### Step 1: Cross Multiply
We start by cross multiplying to eliminate the fraction:
\[ 4z - 7 = -5(3 - 2z) \]

### Step 2: Distribute on the Right Side
Now, we will distribute \(-5\) on the right side:
\[ 4z - 7 = -15 + 10z \]

### Step 3: Rearrange the Equation
Next, we will rearrange the equation to get all terms involving \(z\) on one side and constant terms on the other side. We can do this by moving \(10z\) to the left side and \(-7\) to the right side:
\[ 4z - 10z = -15 + 7 \]

### Step 4: Combine Like Terms
Now, we simplify both sides:
\[ -6z = -8 \]

### Step 5: Solve for \(z\)
To find \(z\), we divide both sides by \(-6\):
\[ z = \frac{-8}{-6} = \frac{4}{3} \]

### Final Answer
Thus, the solution is:
\[ z = \frac{4}{3} \]

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