What number should both sides of the equation x−5=−6

Question

What number should both sides of the equation  x−5=−6
𝑥
−
5
=
−
6
  be multiplied by to solve for the value of  x
𝑥
 ?(1 point)
$$
Check answerRemaining Attempts : 3

GPT-4o mini · Answer

To solve the equation $ x - 5 = -6 $ for $ x $, you can isolate $ x $ without multiplying both sides by any number. Here's how you can do it: 1. Add 5 to both sides of the equation to isolate $ x $: $$ x - 5 + 5 = -6 + 5 $$ This simplifies to: $$ x = -1 $$ So the value of $ x $ is $-1$. If you're specifically looking to multiply both sides by a number, you can technically multiply by any non-zero number (like 1) without changing the equality, but this is not necessary for solving the equation directly. Just isolating $ x $ is the simplest approach.

m · Answer

Your answer is wrong.

GPT-4o mini · Answer

I apologize for any confusion. Let's clarify the steps to solve the equation $x - 5 = -6$.

The equation can be solved by isolating $x$ without necessarily multiplying by a number. Here's the step-by-step solution again:

Start with the original equation: \[ x - 5 = -6 \]
To solve for $x$, add 5 to both sides: \[ x - 5 + 5 = -6 + 5 \]

This reduces to: \[ x = -1 \]

Thus, $x = -1$.

If your question concerns multiplying both sides of the equation by a specific number, it’s important to note that multiplying by any non-zero number does not affect the solution but does complicate it unnecessarily in this case.

If you meant to ask about manipulating the equation in a specific way (like getting rid of fractions or balancing an equation), please provide further context! Otherwise, multiplying both sides of the equation by 1 would keep the equation the same:

\[ 1(x - 5) = 1(-6) \]

This still results in the same equation, $x - 5 = -6$.

Again, I'm here to clarify or assist further if needed!

m · Answer

So what's the answer.

GPT-4o mini · Answer

To answer your original question directly:

The equation $ x - 5 = -6 $ does not require you to multiply both sides by a specific number to solve for $ x $. However, if you were to multiply both sides by any non-zero number, it would preserve the equality.

If you are looking for a specific number to multiply by just to illustrate the process, you could multiply by 1 (which doesn't change the value) or -1 (which flips the signs of both sides), but these aren't necessary to solve the equation.

If we had to choose one number to multiply both sides of $ x - 5 = -6 $, it could be any non-zero number, but a common one to illustrate the point would be 1.

To recap:

You can multiply both sides by any non-zero number, but it’s not needed to find $ x $.
A typical choice could be 1.