Question

(7y-1)/12-(y+1)/4=(2y+5)/3

Answer 1

$\frac{7y-1}{12} - \frac{y+1}{4} = \frac{2y+5}{3} /*12\\ 7y-1-3(y+1)=4(2y+5)\\ 7y-1-3y-3=8y+20\\ 4y-8y=20+4\\ -4y=24/:(-4)\\ y=-6$

Answer 2

To solve the equation (7y-1)/12 - (y+1)/4 = (2y+5)/3, we can simplify the fractions and combine like terms. Here's the step-by-step solution:

Step 1: Find a common denominator for the fractions on both sides of the equation. The common denominator in this case is 12.

(7y-1)/12 - (y+1)/4 = (2y+5)/3 [(7y-1)(4) - (y+1)(12)]/12 = (2y+5)/3

Step 2: Simplify the numerators.

[28y - 4 - (12y + 12)]/12 = (2y+5)/3 [28y - 4 - 12y - 12]/12 = (2y+5)/3 (16y - 16)/12 = (2y+5)/3

Step 3: Simplify both sides of the equation further.

(4(4y - 4))/ (4*3) = (2y+5)/3 (4y - 4)/3 = (2y+5)/3

Step 4: Eliminate the denominators by multiplying both sides by 3.

3 * (4y - 4)/3 = 3 * (2y+5)/3 4y - 4 = 2y + 5

Step 5: Combine like terms.

4y - 2y = 5 + 4 2y = 9

Step 6: Solve for y by dividing both sides by 2.

2y/2 = 9/2 y = 9/2

Therefore, the solution to the equation is y = 9/2 or 4.5.