First, multiply each side of the inequality by #color(red)(2)# to eliminate the fraction while keeping the inequality balanced:
#color(red)(2) xx (7 - 2b)/2 < color(red)(2) xx 3#
#cancel(color(red)(2)) xx (7 - 2b)/color(red)(cancel(color(black)(2))) < 6#
#7 - 2b < 6#
Next, subtract #color(red)(7)# from each side of the inequality to isolate the #b# term while keeping the inequality balanced:
#7 - 2b - color(red)(7) < 6 - color(red)(7)#
#7 - color(red)(7) - 2b < -1#
#0 - 2b < -1#
#-2b < -1#
Now divide each side of the inequality by #color(blue)(-2)# to solve for #b# while keeping the inequality balanced. However, because we are multiplying or dividing an inequality by a negative term we must reverse the inequality sign.
#(-2b)/color(blue)(-2) color(red)(>) (-1)/color(blue)(-2)#
#(color(blue)(cancel(color(black)(-2)))b)/cancel(color(blue)(-2)) color(red)(>) 1/2#
#b > 1/2#
