[tex]5x - 19 \leqslant 1[/tex]
change
[tex] \leqslant \: to \: = [/tex]
given you
[tex]5x - 19 = 1[/tex]
making x the subject by transferring the -19 to the right hand side of the equation
[tex]5x = 19 + 1[/tex]
[tex]5x = 20[/tex]
dividing through by 5
[tex] \frac{5x}{5} = \frac{20}{5} [/tex]
[tex]x = 4[/tex]
{[tex]{x:x \leqslant 4}[/tex]}
also given
[tex] - 4x + 3 < - 6[/tex]
change the operation sign to =
[tex] - 4x + 3 = - 6[/tex]
[tex] - 4x = - 6 - 3[/tex]
[tex] - 4x = - 9[/tex]
dividing through by -4
[tex] \frac{ - 4x}{ - 4} = \frac{ - 9}{ - 4} [/tex]
[tex]x = \frac{9}{4} [/tex]
so the truth set is
{x:x>9/4}.
The < sign changes to > because we divided by a negative number when solving for x
