Solve the following equation.
8−5w=7−3w−2w
(1 point)
Responses
w=1
w is equal to 1
Infinitely Many
Infinitely Many
No Solution
No Solution
To solve the equation 8 - 5w = 7 - 3w - 2w, we can simplify the equation step by step:
1. Distribute the -2 across the terms -3w - 2w to get:
8 - 5w = 7 - 3w - 2w
8 - 5w = 7 - 5w
2. Combine like terms on both sides of the equation:
-5w + 5w = -5w + 5w
0 = 0
After simplifying the equation, we are left with 0 = 0. This equation is always true, which means it has infinitely many solutions.
Therefore, the correct solution is: Infinitely Many.
To solve the given equation 8 - 5w = 7 - 3w - 2w, we follow the steps below:
1. Start by simplifying both sides of the equation by combining like terms. On the left side, combine 8 and -5w to get -5w + 8. On the right side, combine 7, -3w, and -2w to get -5w + 7.
So we have: -5w + 8 = -5w + 7
2. Now we want to isolate the variable w on one side of the equation. To do this, we can subtract -5w from both sides of the equation. This will cancel out the -5w term on both sides.
So we have: -5w + 8 - (-5w) = -5w + 7 - (-5w)
Simplifying further, we get: 8 = 7
3. The last step is to examine the equation 8 = 7. Here, we can see that both sides of the equation are not equal. In other words, there is no value of w that makes this equation true.
Therefore, the answer is "No Solution."