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

1 answer

To determine why the equation \(-5 = \frac{4 - 3x}{4 - 3x}\) might be undefined, we need to examine the fraction on the right side, \(\frac{4 - 3x}{4 - 3x}\).

This expression is undefined when the denominator is equal to zero. Therefore, we need to find the value of \(x\) that makes the denominator \(4 - 3x\) equal to zero:

\[ 4 - 3x = 0 \]

Solving for \(x\):

\[ 3x = 4 \ x = \frac{4}{3} \]

Thus, the equation \(-5 = \frac{4 - 3x}{4 - 3x}\) is undefined specifically when \(x = \frac{4}{3}\). At this value, both the numerator and the denominator become zero, leading to an indeterminate form \( \frac{0}{0} \). Therefore, the original equation is undefined for \(x = \frac{4}{3}\).