Question

1/3(y - 2) -5/6 (y + 1) =3/4 (y - 3) - 2

Answer 1

Answer:

$y=\frac{11}{5}$

Step-by-step explanation:

Given expression

$\frac{1}{3}(y-2)-\frac{5}{6}(y+1)=\frac{3}{4}(y-3)-2$

To solve for $y$ for the given expression.

Solution:

We multiply each term with the least common multiple of the denominators of the fraction in order to remove fractions.

The multiples of the denominators are:

3 = 3,6,9,12,15

6 = 6,12

4 = 4,8,12

The least common multiple = 12.

Multiplying each term with 12.

$12.\frac{1}{3}(y-2)-12.\frac{5}{6}(y+1)=12.\frac{3}{4}(y-3)-2(12)$

$4(y-2)-10(y+1)=9(y-3)-24$

Using distribution.

$4y-8-10y-10=9y-27-24$

Simplifying.

$-6y-18=9y-51$

Adding $6y$ both sides.

$-6y+6y-18=9y+6y-51$

$-18=15y-51$

Adding 51 both sides.

$-18+51=15y-51+51$

$33=15y$

Dividing both sides by 15.

$\frac{33}{15}=\frac{15y}{15}$

$\frac{33}{15}=y$

Simplifying fractions.

$\frac{11}{5}=y$

∴ $y=\frac{11}{5}$  (Answer)