Question
Determine whether the statement is sometimes, always, or never true. If ax + b - 4 = b and a # 0 then x = 4/a
Answers
GPT-4o
To determine whether the statement "If \( ax + b - 4 = b \) and \( a \neq 0 \) then \( x = \frac{4}{a} \)" is sometimes, always, or never true, let's work through the given equation step by step.
The given equation is:
\[ ax + b - 4 = b \]
First, simplify the equation by subtracting \( b \) from both sides:
\[ ax + b - 4 - b = b - b \]
\[ ax - 4 = 0 \]
Next, isolate \( x \) by adding 4 to both sides:
\[ ax = 4 \]
Now, solve for \( x \) by dividing both sides by \( a \) (and noting that \( a \neq 0 \)):
\[ x = \frac{4}{a} \]
Thus, we find that \( x = \frac{4}{a} \).
Since our steps logically follow from the original equation and there are no conditions or special cases that would cause deviation, the statement "If \( ax + b - 4 = b \) and \( a \neq 0 \), then \( x = \frac{4}{a} \)" is always true.
The given equation is:
\[ ax + b - 4 = b \]
First, simplify the equation by subtracting \( b \) from both sides:
\[ ax + b - 4 - b = b - b \]
\[ ax - 4 = 0 \]
Next, isolate \( x \) by adding 4 to both sides:
\[ ax = 4 \]
Now, solve for \( x \) by dividing both sides by \( a \) (and noting that \( a \neq 0 \)):
\[ x = \frac{4}{a} \]
Thus, we find that \( x = \frac{4}{a} \).
Since our steps logically follow from the original equation and there are no conditions or special cases that would cause deviation, the statement "If \( ax + b - 4 = b \) and \( a \neq 0 \), then \( x = \frac{4}{a} \)" is always true.