Question

Consider the equation below.

3/4 (24 – 16x) = - Î (18x – 27)
How many solutions does the equation have?
(A) one, x = 0
B
one, x = -27/8
C) no solutions
D) infinitely many solutions​

Answer 1

The equation has no solutions .

Explanation:

Given as :

The linear equation is

`(3)/(4)`(24 -16 x) =
`(-2)/(3)`(18 x -27)

Or,
`(3)/(4)` ×24 -
`(3)/(4)` × 16 x =
`(-2)/(3)` × 18 x -
`(-2)/(3)` × 27

Or,
`(3)/(4)` ×24 -
`(3)/(4)` × 16 x =
`(-2)/(3)` × 18 x +
`(2)/(3)` × 27

Or,
`(3* 24)/(4)` -
`(3* 16 x)/(4)` =
`(-2* 18 x)/(3)` +
`(2* 27 x)/(3)`

Or, 3 × 6 - 3 × 4 x = - 2 × 6 x + 2 × 9

Or, 18 - 12 x = - 12 x + 18

Or, 18 - 18 = - 12 x + 12 x

or, 0 = 0

∵ The linear equation has no variables , so the equation has no solution

Hence,The equation has no solutions . Answer