Question

8−5w=7−3w−2w

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve the equation, we need to simplify and combine like terms on both sides.

Starting with the left side of the equation, we have 8 - 5w.

On the right side, we have 7 - 3w - 2w.

Combining like terms on the right side, we have 7 - (3w + 2w) = 7 - 5w.

So the equation becomes:

8 - 5w = 7 - 5w.

Now, we can see that both sides of the equation are the same, so there are infinitely many solutions.

Answer 2

[AI-generated answer — Step-by-Step Bot]

To solve the equation 8−5w=7−3w−2w, we need to simplify and combine like terms on both sides of the equation.

Let's start by simplifying the expressions:

8−5w can be rewritten as -5w + 8.

7−3w−2w can be rewritten as -3w - 2w + 7.

Now, let's substitute the simplified expressions back into the equation:

-5w + 8 = -3w - 2w + 7

Next, let's combine like terms on both sides of the equation:

Combine the -5w, -3w, and -2w terms on the left side:

(-5w - 3w - 2w) + 8 = 7

Combine the -5w, -3w, and -2w terms to get:

-10w + 8 = 7

Then, subtract 8 from both sides to isolate the variable:

-10w = 7 - 8

Simplifying the right side gives:

-10w = -1

Finally, divide both sides of the equation by -10 to solve for w:

w = -1 / -10

Simplifying the right side gives:

w = 1/10

So, the solution to the equation is w = 1/10.

Answer 3

[AI-generated answer — Explain Bot]

To solve the equation 8 - 5w = 7 - 3w - 2w, we want to simplify and combine like terms on both sides of the equation.

Starting with the left side, we have 8 - 5w. There are no like terms to combine in this expression, so we can leave it as is.

Moving to the right side, we have 7 - 3w - 2w. We can combine the terms with the variable w together. -3w - 2w can be simplified to -5w. Therefore, the right side becomes 7 - 5w.

Now our equation becomes 8 - 5w = 7 - 5w.

At this point, we can observe that the variables are the same on both sides of the equation. When the variables are the same, it means that the equation is either true for all values of the variable or false for all values of the variable.

To determine which case it is, we can subtract the same term from both sides of the equation in order to isolate the variables.

Subtracting -5w from both sides of the equation, we get:

(8 - 5w) - (-5w) = (7 - 5w) - (-5w)

This simplifies to:

8 - 5w + 5w = 7 - 5w + 5w

On the left side, the -5w and +5w will cancel each other out, leaving us with just 8. On the right side, the same thing happens, resulting in just 7.

So now our equation becomes:

8 = 7

Since 8 is not equal to 7, we have a contradiction. Therefore, there is no solution to this equation.