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 $4-3x=0$:

$$4-3x=0⟹3x=4⟹x=\frac{4}{3}$$

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.