[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