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

$\frac{5x}{5} = \frac{20}{5}$

$x = 4$

{${x:x \leqslant 4}$}

also given

$- 4x + 3 < - 6$

change the operation sign to =

$- 4x + 3 = - 6$

$- 4x = - 6 - 3$

$- 4x = - 9$

dividing through by -4

$\frac{ - 4x}{ - 4} = \frac{ - 9}{ - 4}$

$x = \frac{9}{4}$

so the truth set is

{x:x>9/4}.

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