Question

What makes the equation -5 = 4 – 3x over 4–3x undefined?

Answer 1

To determine when the equation \(-5 = 4 - 3x\) can be considered undefined, we should first note that the expression for \(4 - 3x\) is not inherently undefined; rather, an equation becomes undefined when we encounter a situation where division by zero occurs or when a logarithm of a non-positive number is involved. However, in this case, the equation itself does not contain such operations.

Let's analyze the equation:

\[
-5 = 4 - 3x
\]

To solve for \(x\), we can rearrange the equation:

1. Subtract 4 from both sides:

\[
-5 - 4 = -3x
\]

This simplifies to:

\[
-9 = -3x
\]

2. Divide both sides by -3:

\[
x = \frac{9}{3}
\]

This gives:

\[
x = 3
\]

Now, there is nothing about \(x = 3\) that is undefined. However, if we had more complex expressions involving division, such as \( \frac{1}{4 - 3x} \), we would want to investigate when that expression might be undefined.

In that case, we would determine when \(4 - 3x = 0\):

\[
4 - 3x = 0 \implies 3x = 4 \implies x = \frac{4}{3}
\]

At \(x = \frac{4}{3}\), the expression would be undefined due to division by zero.

In summary, the original equation \(-5 = 4 - 3x\) does not become undefined at any point. It only leads to \(x = 3\). If we had an operation such as division by \(4 - 3x\) in a larger expression, we would check when \(4 - 3x\) equals zero; that would be the situation to consider for undefined behavior.