1/3(y+4)+6=1/4(3y-1)-2 show work Please
(y+4)/3 + 6 = (3y-1)/4 - 2
4(y+4)/12 + 6 = 3(3y-1)/12 - 2
(4y+16)/12 + 6 = (9y-3)/12 - 2
Multiply both sides by 12:
4y + 16 + 72 = 9y - 3 - 24
4y - 9y = -27 -88
-5y = -115
Y = 23
To solve the equation 1/3(y+4)+6 = 1/4(3y-1)-2, we need to follow several steps:
Step 1: Distribute the fractions.
Start by distributing the fraction 1/3 and 1/4 to their respective terms. This means multiplying each term inside the parentheses by the denominator.
(1/3) * (y+4) + 6 = (1/4) * (3y-1) - 2
(y/3 + 4/3) + 6 = (3y/4 - 1/4) - 2
Step 2: Combine like terms.
Combine the terms 4/3 and 6 on the left-hand side, as well as -1/4 and -2 on the right-hand side.
y/3 + 4/3 + 6 = 3y/4 - 1/4 - 2
y/3 + 22/3 = 3y/4 - 9/4
Step 3: Clear the fractions.
To eliminate the fractions, we can multiply all the terms in the equation by the least common denominator (LCD), which is 12.
12 * (y/3 + 22/3) = 12 * (3y/4 - 9/4)
4y + 44 = 9y - 27
Step 4: Simplify and solve for y.
Combine like terms on both sides of the equation.
4y - 9y = -27 - 44
-5y = -71
Divide both sides by -5 to solve for y.
y = (-71)/(-5)
Finally, simplify the division to find the value of y.
y = 71/5
Therefore, the solution to the given equation is y = 71/5.