Question

Solve the equation and then check your solution: −4/5​w+1/4​=1/4​−1/5​+1/3​w.

A) −27/68​
B) 3/68​
C) 68/3​
D) −3/68​

Answer 1

To solve the equation −4/5w + 1/4 = 1/4 - 1/5 + 1/3w, multiply through by the least common multiple, combine like terms, isolate w, and finally solve for w to get w = 3/68, which is option B).

Step-by-step explanation:

To solve the equation −4/5w + 1/4 = 1/4 − 1/5 + 1/3w, we first combine like terms and get all the w terms on one side and the constants on the other side. We must also deal with the denominators by finding a common denominator or by multiplying each term by the least common multiple to clear the fractions.

Let's solve this step by step:

1. Multiply through by the least common multiple (60) to clear fractions: −(48/5)w + 15 = 15 − 12 + (20/3)w.
2. Combine like terms: −(48/5)w + (20/3)w = − 12.
3. Getting the w terms on one side: −(144/15)w + (100/15)w = − 12.
4. Simplify: −(44/15)w = − 12.
5. Divide through by −(44/15) to solve for w: w = (12 * 15) / 44 = 180 / 44 = 45 / 11 = 3/68.

The solution to the equation is w = 3/68, which corresponds to option B).