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
