Question
Consider the equation
For which value of 8x-6=3-k+8x does this equation have infinitely many solutions?
k=?
For which value of 8x-6=3-k+8x does this equation have infinitely many solutions?
k=?
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To determine the value of \( k \) for which the equation \( 8x - 6 = 3 - k + 8x \) has infinitely many solutions, we need to analyze the structure of the equation.
First, we can simplify the equation. We can start by subtracting \( 8x \) from both sides:
\[
8x - 6 - 8x = 3 - k + 8x - 8x
\]
This simplifies to:
\[
-6 = 3 - k
\]
Next, we can isolate \( k \):
\[
-6 - 3 = -k
\]
\[
-9 = -k
\]
\[
k = 9
\]
For the equation \( 8x - 6 = 3 - k + 8x \) to have infinitely many solutions, the left-hand side must be equal to the right-hand side for all \( x \). This happens when the expressions on both sides are identical for all \( x \).
Since we simplified to \( -6 = 3 - k \), this shows that if \( k = 9 \), the two sides are indeed equal, resulting in an equation that holds for all values of \( x \).
Thus, the answer is:
\[
\boxed{9}
\]
First, we can simplify the equation. We can start by subtracting \( 8x \) from both sides:
\[
8x - 6 - 8x = 3 - k + 8x - 8x
\]
This simplifies to:
\[
-6 = 3 - k
\]
Next, we can isolate \( k \):
\[
-6 - 3 = -k
\]
\[
-9 = -k
\]
\[
k = 9
\]
For the equation \( 8x - 6 = 3 - k + 8x \) to have infinitely many solutions, the left-hand side must be equal to the right-hand side for all \( x \). This happens when the expressions on both sides are identical for all \( x \).
Since we simplified to \( -6 = 3 - k \), this shows that if \( k = 9 \), the two sides are indeed equal, resulting in an equation that holds for all values of \( x \).
Thus, the answer is:
\[
\boxed{9}
\]
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