Final answer:
To solve the equation 1/6 + 1 - 3q = 2 - 4q + 1/8, combine like terms, isolate the variable q, and simplify the equation. The value of q is 23/24, and it is negative.
Step-by-step explanation:
To solve the equation 1/6 + 1 - 3q = 2 - 4q + 1/8, we need to simplify the equation by combining like terms and isolating the variable q.
First, let's combine the constants and the fractions on both sides of the equation:
- On the left side, 1/6 + 1 can be simplified to (1/6 + 6/6) = 7/6.
- On the right side, 2 + 1/8 can be simplified to (2 + 1/8) = 17/8.
Now, let's gather the terms with q on one side and the constant terms on the other side. We can subtract 17/8 and add 3q to both sides of the equation:
To simplify the left side of the equation, we need to find a common denominator for 6 and 8, which is 24:
- (7/6)*(4/4) - (17/8)*(3/3) = 3q - 4q
- 28/24 - 51/24 = 3q - 4q
- -23/24 = -q
To find q, we can multiply both sides by -1:
The value of q is 23/24. The arithmetic sign (-) means that q is negative.