# How would i solve this linear equation? 10+7y/4=5-y/3

could you include some details thanks

Multiply each side by least common denominator.

lcd of 3,4 is 12.

12(10+7y/4)=12(5-y/3)

120+21y=60-4y

120+21y+4y=60-4y+4y

120+25y=60

subtract 120 from each side

120-120+25y=60-120

25y=-60

Divide each side by 25

25y/25=-60/25

y=-2.4

Multiply each side by least common denominator.

lcm of 3,4 is 12.

12(10+7y/4)=12(5-y/3)

120+21y=60-4y

120+21y+4y=60-4y+4y

120+25y=60

subtract 120 from each side

120-120+25y=60-120

25y=-60

Divide each side by 25

25y/25=-60/25

= -2.4

The linear equation is 10 + 7y/4 = 5 - y/3.

10 + 7y/4 + y/3 = 5

Subtract 10 from each side.

7y/4 + y/3 = 5 - 10

7y/4 + y/3 = - 5

Fractions with different denominators can not be added. So, write the equation with common denominator.

Find the least common denominator L.C.M.

Multiples of 4 = 4, 8, 12, 16 ......

Multiples of 3 = 3, 6, 9, 12, 15, .......

Least Common Multiple of 4 and 3 is 12.

Write the right hand side equation with common denominator.

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

y[ 21/12 + 4/12 ] = - 5

Since denominators are same add the numerators over the denominator.

y(25/12) = - 5

Divide each side by 25/12.

y = - 5/(25/12) = -12/5.

Solution is y = - 12/5.