Question

Solve for x. 5 x − 19 ≤ 1 OR − 4 x + 3 < − 6

Answer 1

`5x - 19 \leqslant 1`

change

`\leqslant \: to \: =`

given you

`5x - 19 = 1`

making x the subject by transferring the -19 to the right hand side of the equation

`5x = 19 + 1`

`5x = 20`

dividing through by 5

`(5x)/(5) = (20)/(5)`

`x = 4`

{
`{x:x \leqslant 4}`}

also given

`- 4x + 3 < - 6`

change the operation sign to =

`- 4x + 3 = - 6`

`- 4x = - 6 - 3`

`- 4x = - 9`

dividing through by -4

`( - 4x)/( - 4) = ( - 9)/( - 4)`

`x = (9)/(4)`

so the truth set is

{x:x>9/4}.

The < sign changes to > because we divided by a negative number when solving for x