First, expand the terms within parenthesis on the right side of the inequality by multiplying each term within the parenthesis by the term outside the parenthesis:
#49 >= color(red)(-7)(v - 9)#
#49 >= (color(red)(-7) xx v) - (color(red)(-7) xx 9)#
#49 >= -7v - (-63)#
#49 >= -7v + 63#
Next, subtract #color(red)(63)# from each side of the inequality to isolate the #v# term while keeping the inequality balanced:
#49 - color(red)(63) >= -7v + 63 - color(red)(63)#
#-14 >= -7v + 0#
#-14 >= -7v#
Now, divide each side of the inequality by #color(blue)(-7)# to solve for #v# while keeping the inequality balanced. However, because we are multiplying or dividing an inequality by a negative term we must reverse the inequality operator:
#(-14)/color(blue)(-7) color(red)(<=) (-7v)/color(blue)(-7)#
#2 color(red)(<=) (color(blue)(cancel(color(black)(-7)))v)/cancel(color(blue)(-7))#
#2 <= v#
To state the solution in terms of #v# we can reverse or "flip" the entire inequality:
#v >= 2#
