Question

Would really appreciate someone’s help

Answer 1

see explanation

Explanation:

(a)

4(m + 1) - (m - 1) = 20 ← distribute parenthesis

4m + 4 - m + 1 = 20

3m + 5 = 20 ( subtract 5 from both sides )

3m = 15 ( divide both sides by 3 )

m = 5

(b)

(4k - 1)(3k + 6) = 0

equate each factor to zero and solve for k

4k - 1 = 0 ( add 1 to both sides )

4k = 1 ( divide both sides by 4 )

k =
`(1)/(4)`

3k + 6 = 0 ( subtract 6 from both sides )

3k = - 6 ( divide both sides by 3 )

k = - 2

solutions are k = - 2 , k =
`(1)/(4)`

(c)

`((2y-1))/(5)` = 1
`(3)/(4)` -
`(2-y)/(2)` ← change mixed number to improper fraction

`((2y-1))/(5)` =
`(7)/(4)` -
`(2-y)/(2)`

multiply through by 20 ( the LCM of 5, 4 and 2 ) to clear the fractions

4(2y - 1) = 35 - 10(2 - y) ← distribute parenthesis on both sides

8y - 4 = 35 - 20 + 10y ( subtract 10y from both sides )

- 2y - 4 = 15 ( add 4 to both sides )

- 2y = 19 ( divide both sides by - 2 )

y = -
`(19)/(2)` = - 9.5