Question

Question To solve the equation 23(x−4)=−10 , Izzy wants to multiply both sides of the equation by the reciprocal of the fraction. Name the reciprocal.


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Answer 1

wrong

Answer 2

To solve the equation \( 23(x - 4) = -10 \), Izzy can multiply both sides by the reciprocal of the coefficient of the term \( (x - 4) \). The coefficient here is 23.

The reciprocal of 23 is \( \frac{1}{23} \).

So, the reciprocal that Izzy wants to use is \( \frac{1}{23} \).

Answer 3

I apologize for any confusion. Let's clarify the problem step by step.

The equation given is:

\[
23(x - 4) = -10
\]

If we isolate \( (x - 4) \) by dividing both sides by \( 23 \), we get:

\[
x - 4 = \frac{-10}{23}
\]

In this context, if Izzy wants to multiply both sides of the equation by the reciprocal of the fraction on the right side, the fraction is \( \frac{-10}{23} \).

The reciprocal of \( \frac{-10}{23} \) is:

\[
\frac{23}{-10} \quad \text{or} \quad -\frac{23}{10}
\]

So, the correct reciprocal of the fraction \( \frac{-10}{23} \) is \( -\frac{23}{10} \). Thank you for your patience, and I'm sorry for any confusion in my previous response!