Solve the equation 8 - 5w = 7 - 3w - 2w Show your work. Choose the correct answer from the following
a) w = 1
b) Infinitely many
c) No solution
To solve the equation, we need to combine like terms on both sides of the equation.
Starting with the left side:
8 - 5w
Now, moving on to the right side:
7 - 3w - 2w
Combining like terms on the right side:
7 - 5w
Now our equation looks like this:
8 - 5w = 7 - 5w
We can see that both sides of the equation are identical, meaning they are equal for any value of w. In other words, no matter what value we choose for w, the equation will be true.
Therefore, the correct answer is b) Infinitely many solutions.
To solve the equation 8 - 5w = 7 - 3w - 2w, we can start by simplifying both sides of the equation.
On the left side, the only term is 8 - 5w.
On the right side, we have 7 - 3w - 2w. We can combine the like terms -3w and -2w to get -5w. Therefore, the right side simplifies to 7 - 5w.
Now we have the equation 8 - 5w = 7 - 5w.
Next, let's isolate the variable w. We can do this by moving all terms with w to one side of the equation.
Subtracting -5w from both sides, we have 8 - 5w + 5w = 7 - 5w + 5w.
Simplifying further, we get 8 = 7.
However, we see that the equation simplifies to a false statement, 8 = 7, which means there is no solution.
Therefore, the correct answer is:
c) No solution
To solve the equation 8 - 5w = 7 - 3w - 2w, we need to simplify both sides of the equation and isolate the variable w on one side.
First, let's simplify the right side of the equation by combining like terms:
7 - 3w - 2w = 7 - 5w
Now, we can rewrite the equation as:
8 - 5w = 7 - 5w
Notice that the variable w appears on both sides of the equation. To isolate w, we need to bring all terms containing w to one side of the equation. We can do this by subtracting -5w from both sides:
(8 - 5w) + 5w = (7 - 5w) + 5w
Simplifying further, we get:
8 = 7
At this point, we can see that the equation is inconsistent and cannot be true. This means that there are no solutions for the given equation. Therefore, the correct answer is:
c) No solution