Question

What is the value of x in the equation below?

-2/3 (3/8x + 9)= 3/5(5/12x+10)
A -1
B 0
C 5-
D 3

Answer 1

`\sf - (2)/(3) ( (3)/(8) x + 9) = (3)/(5) ( (5)/(12) x + 10)`

• Multiply both sides of the equation by 15.

`\sf \: - 10( (3)/(8) x + 9) = 9( (5)/(12) x + 10)`

• Distribute -10 through the parentheses.

`\sf \: - (15)/(4) x - 90 = 9( (5)/(12) x + 10)`

• Distribute 9 through the parentheses.

`\sf \: - (15)/(4) x - 90 = (15)/(4) x + 90`

• Multiply both sides of the equation by 4.

`\sf \: - 15x - 360 = 15x + 360`

• Move the variable to the left-hand side and change its sign.

`\sf \: - 15x - 360 - 15x = 360`

• Move the constant to the right-hand side and change its sign.

`\sf \: - 15x - 15x = 360 + 360`

• Collect like terms.

`\sf \: - 30x = 720`

• Divide both sides of the equation by-30.

`\boxed{ \tt \: x = - 24}`

Answer 2

x = - 24

Explanation:

-
`(2)/(3)` (
`(3)/(8)` x + 9) =
`(3)/(5)` (
`(5)/(12)` x + 10) ← distribute parenthesis on both sides

-
`(1)/(4)` x - 6 =
`(1)/(4)` x + 6 ( multiply through by 4 to clear the fractions )

- x - 24 = x + 24 ( subtract x from both sides )

- 2x - 24 = 24 ( add 24 to both sides )

- 2x = 48 ( divide both sides by - 2 )

x = - 24