Solve the following equation 8 - 5w = 7 - 3w - 2w Choose the correct answer from the following a) w = 1 b) Infinitely Many c) No Solution
To solve the equation, we can combine like terms on the right side of the equation:
8 - 5w = 7 - 3w - 2w
8 - 5w = 7 - 5w
Since the variable terms on both sides of the equation cancel out, we are left with:
8 = 7
Since this equation is not true, there is no solution. Therefore, the correct answer is c) No Solution.
To solve the equation 8 - 5w = 7 - 3w - 2w, we can simplify and combine like terms on each side:
8 - 5w = 7 - 5w.
By subtracting 7 from both sides, we get:
8 - 7 - 5w = 7 - 7 - 5w,
1 - 5w = 0.
By adding 5w to both sides, we get:
1 - 5w + 5w = 0 + 5w,
1 = 5w.
Dividing both sides by 5, we have:
(1/5) = (5w)/(5),
1/5 = w.
So, the solution to the equation is w = 1/5.
Therefore, the correct answer is: w = 1/5.
To solve the given equation, we need to simplify both sides and then combine like terms to isolate the variable w. Let's solve it step by step:
8 - 5w = 7 - 3w - 2w
First, simplify the constants on both sides:
8 - 5w = 7 - 5w
Next, combine like terms:
-5w + 5w = -5w
On the left side, the 5w and -5w cancel each other out, leaving us with 0:
0 = -5w
Now, we can conclude that this equation has no solution. This is because the equation 0 = -5w implies that 0 is equal to a non-zero value. Since this is not possible, the equation has no solution.
Therefore, the correct answer is:
c) No Solution