Question

Find x and m: `(3x - 2)/4 - ((x - 3))/5` = −1

Answer 1

Taking L.C.M on L.H.S

`((3x - 2) xx 5 - (x - 3))/20` ...[L.C.M of 4 and 5 is 20]

Expanding brackets,

`(3x xx 5 - 2 xx 5 - x xx 4 - (-3) xx 4)/20` = −1

`(15x - 10 - 4x - (-12))/20` = −1

`(15x - 10 - 4x + 12)/20` = −1

⇒ `(11x + 2)/20` = −1

Multiplying both sidesby 20

`(11x + 2)/20 xx 20` = −1 × 20

∴ 11x + 2 = − 20

∴ 11x = − 20 − 2 = − 22

x = `(-22)/11`

= − 2

∴ x = − 2