Question

what makes -5 = 4 - (3x/4) - 3x undefied

Answer 1

To determine if the equation \(-5 = 4 - \frac{3x}{4} - 3x\) has any undefined values, let's first simplify the right-hand side.

We start with:
\[
-5 = 4 - \frac{3x}{4} - 3x
\]

We can combine the terms on the right side. The term \(-3x\) can be rewritten to a common denominator of 4:
\[
-3x = -\frac{12x}{4}
\]

Now, substituting this back gives:
\[
-5 = 4 - \frac{3x}{4} - \frac{12x}{4}
\]

Combining the \(x\) terms:
\[
-5 = 4 - \frac{15x}{4}
\]

We can isolate the \(x\) term to one side. First, subtract 4 from both sides:
\[
-5 - 4 = -\frac{15x}{4}
\]
\[
-9 = -\frac{15x}{4}
\]

Next, multiply both sides by -1:
\[
9 = \frac{15x}{4}
\]

Now, multiply both sides by \(4\) to eliminate the fraction:
\[
36 = 15x
\]

Finally, divide both sides by \(15\):
\[
x = \frac{36}{15} = \frac{12}{5}
\]

The equation has a specific solution \(x = \frac{12}{5}\).

This analysis reveals that \(-5 = 4 - \frac{3x}{4} - 3x\) is not undefined. It is a defined linear equation. There are no restrictions on \(x\) that would cause the expression to be undefined for any real number, and the equation can be solved for \(x\) as shown. Thus, there are no undefined values in this equation.