https://file.aiquickdraw.com/mathbot/file/1725483990441l1l8cxn0.jpg

The given mathematical expression is:

\[
\frac{16x - 12}{24} \times \frac{14}{2 - 3x}
\]

To simplify this expression, let's go through it step by step.

### Step 1: Simplify the first fraction
The first fraction is:

\[
\frac{16x - 12}{24}
\]

We can factor out the common factor of \(4\) from the numerator:

\[
\frac{4(4x - 3)}{24} = \frac{4x - 3}{6}
\]

### Step 2: Multiply the fractions
Now we multiply the simplified first fraction by the second fraction:

\[
\frac{4x - 3}{6} \times \frac{14}{2 - 3x}
\]

### Step 3: Multiply the numerators and denominators
The product of the fractions is:

\[
\frac{(4x - 3) \times 14}{6 \times (2 - 3x)} = \frac{14(4x - 3)}{6(2 - 3x)}
\]

### Step 4: Simplify the expression
We can simplify the fraction further by dividing both the numerator and denominator by 2:

\[
\frac{7(4x - 3)}{3(2 - 3x)}
\]

Thus, the simplified form of the expression is:

\[
\frac{7(4x - 3)}{3(2 - 3x)}
\]

Would you like more details or have any further questions?

### Follow-up Questions:
1. How would you solve for \(x\) if the expression is set equal to zero?
2. Can this expression be simplified further for specific values of \(x\)?
3. What are the restrictions on \(x\) for the original expression to be valid?
4. How would you approach this problem if it were part of a larger equation?
5. How does factoring help in simplifying complex algebraic expressions?

### Tip:
When simplifying expressions, always look for common factors in the numerator and denominator that can be canceled out to make your calculations easier.

Simplify the mathematical expression \(\frac{16x - 12}{24} \times \frac{14}{2 - 3x}\).

Learn how to simplify the algebraic expression \(\frac{16x - 12}{24} \times \frac{14}{2 - 3x}\) step by step. This problem covers key algebraic concepts, including the simplification of fractions and factoring. Suitable for students in Grades 9-11.

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