Question

Solve for the given variable 1) 7(y + 3) = 5y + 82) 4(3r + 5) = -8(2r + 1)3) 19/4 - 7/2a = -1/4a + 3/2

Answer 1

1) 7(y + 3) = 5y + 8

distributing,

7(y) + 7(3) = 5y + 8

7y + 21 = 5y + 8

5y is adding on the right, then it will subtract on the left

21 is adding on the left, then it will subtract on the right

7y - 5y = 8 - 21

2y = -13

2 is multiplying on the left, then it will divide on the right

y = -13/2

2) 4(3r + 5) = -8(2r + 1)

distributing,

4(3r) + 4(5) = -8(2r) + 8(1)

12r + 20 = -16r + 8

16r is subtracting on the right, then it will add on the left

20 is adding on the left, then it will subtract on the right

12r + 16r = 8 - 20

28r = -12

r = -12/28

r = -3/7

3)

`(19)/(4)-(7)/(2)a=-(1)/(4)a+(3)/(2)`

7/2a is subtracting on the left, then it will add on the right

3/2 is adding on the right, then it will subtract on the left

`\begin{gathered} (19)/(4)-(3)/(2)=(1)/(4)a+(7)/(2)a \\ (19-3\cdot2)/(4)=(1+7\cdot2)/(4)a \\ (13)/(4)=(15)/(4)a \end{gathered}`

15/4 is multiplying on the right, then it will divide on the left

`\begin{gathered} (13)/(4)\cdot(4)/(15)=a \\ (13)/(15)=a \end{gathered}`