Answer:
The solution to the equation (5/6)w - (3/4) = (1/3) is w = 169/60 or w ≈ 2.8167 (rounded to four decimal places).
Explanation:
To solve the equation (5/6)w - (3/4) = (1/3), we can follow these steps:
Step 1: Simplify the fractions, if necessary.
The fractions in the equation are already simplified, so we can move on to the next step.
Step 2: Get rid of any constants or terms without w.
In this equation, we have a constant term on the right side, which is (1/3). We need to isolate the term with w on one side of the equation.
To do that, we can move the constant term to the other side of the equation by adding (3/4) to both sides:
(5/6)w - (3/4) + (3/4) = (1/3) + (3/4)
Simplifying both sides of the equation:
(5/6)w = (4/12) + (9/12)
(5/6)w = (13/12)
Step 3: Solve for w.
To solve for w, we need to isolate it on one side of the equation. In this case, we have (5/6) multiplying w.
To remove the (5/6) coefficient, we can multiply both sides of the equation by the reciprocal of (5/6), which is (6/5):
(6/5) * (5/6) * w = (6/5) * (13/12)
Simplifying both sides of the equation:
w = (78/30) * (13/12)
w = 78/30 * 13/12
w = 1014/360
w = 169/60
Therefore, the solution to the equation (5/6)w - (3/4) = (1/3) is w = 169/60 or w ≈ 2.8167 (rounded to four decimal places).