First, multiply each side of the inequality by #color(red)(12)# to eliminate the fraction while keeping the inequality balanced. Eliminating the fraction will make it easier to work with the inequality and #color(red)(12)# is the least common denominator of the two fractions:
#color(red)(12)(-1/3 + 2z) > color(red)(12) xx -3/4#
#(color(red)(12) xx -1/3) + (color(red)(12) xx 2z) > -36/4#
#-12/3 + 24z > -9#
#-4 + 24z > -9#
Next, add #color(red)(4)# to each side of the inequality to isolate the #z# term while keeping the inequality balanced:
#color(red)(4) - 4 + 24z > color(red)(4) - 9#
#0 + 24z > -5#
#24z > -5#
Now, divide each side of the inequality by #color(red)(24)# to solve for #z# while keeping the inequality balanced:
#(24z)/color(red)(24) > -5/color(red)(24)#
#(color(red)(cancel(color(black)(24)))z)/cancel(color(red)(24)) > -5/24#
#z > -5/24#
