Remember that the SAT doesn't ask you to show your work. If you find the algeba in a question challenging, there is often another way to get to the answer. Try this question first using algebra and then using the picking numbers startegy you alermed in chapter 3. Time yourself. Which approach fo you find easier? Which onw was faster ? Did you get the correct answer both times ? Remamber you per-ferred approach and try it first if you see a questin like this on test day.
`(2 (a-3))/(b) =4/7`
If the equation above is true, whihc of the following must NOT be true ?

Options

A. `(b)/(a-3) =7/2`
B. `(2a)/(b ) = -(10)/(7)`
C. `14a -4b=42`
D. `(a-3)/(b) =2/7`

Explanation

To solve the equation \((2(a-3))/(b) = 4/7\) and determine which of the following statements must NOT be true, we can follow these steps:

### Step 1: Cross-Multiply
Start by cross-multiplying the equation to eliminate the fraction:

\[ 2(a - 3) \cdot 7 = 4 \cdot b \]

### Step 2: Simplify the Equation
Distributing the 7 on the left side gives:

\[ 14(a - 3) = 4b \]

### Step 3: Expand and Rearrange
Now, expand the left side:

\[ 14a - 42 = 4b \]

Rearranging this gives us:

\[ 14a - 4b = 42 \]

### Step 4: Analyze the Equation
This equation can be analyzed to find relationships between \(a\) and \(b\). We can express \(b\) in terms of \(a\):

\[ 4b = 14a - 42 \implies b = \frac{14a - 42}{4} = \frac{7a - 21}{2} \]

### Step 5: Check the Statements
Now, we need to evaluate the statements provided in the question to determine which one must NOT be true.

1. **Statement A**: \(a - 3 = \frac{2b}{7}\) - This can be derived from our equation.
2. **Statement B**: \(b = \frac{7}{2}(a - 3)\) - This is equivalent to our derived equation, so it is true.
3. **Statement C**: \(7a - 2b = 21\) - This can be derived from rearranging our equation.
4. **Statement D**: \(b = \frac{2}{7}(a - 3)\) - This does not hold true based on our derived relationships.

### Conclusion
From our analysis, the statement that must NOT be true is **Statement D**.