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4x-32 kx=53
In the given equation,
k is a constant. The equation has no solution. What is the value of
k ?

$4 x-32 k x=53$ $\newline$ In the given equation, $k$ is a constant. The equation has no solution. What is the value of $k$ ?

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Write and solve direct variation equations

Full solution

Q.

4 x-32 k x=53

\newline

In the given equation,

k

is a constant. The equation has no solution. What is the value of

k

?

Analyze Equation: Analyze the given equation. $\newline$ The equation is $4x - 32kx = 53$ . We are told that the equation has no solution. This means that the left side of the equation must not be equal to the right side for any value of $x$ . This can only happen if the coefficient of $x$ on the left side is zero and the constant term is non-zero, because a non-zero coefficient of $x$ would allow for a solution when $x$ is appropriately chosen.
Set Coefficient to Zero: Set the coefficient of $x$ to zero. $\newline$ For the equation to have no solution, the coefficient of $x$ must be zero. The coefficient of $x$ in the equation is $4 - 32k$ . Set this equal to zero to find the value of $k$ . $\newline$ $4 - 32k = 0$
Solve for k: Solve for k. $\newline$ Now, solve the equation for $k$ . $\newline$ $4 = 32k$ $\newline$ Divide both sides by $32$ to isolate $k$ . $\newline$ $k = \frac{4}{32}$ $\newline$ $k = \frac{1}{8}$

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