First, expand the terms in parenthesis by multiplying each term within the parenthesis by the term outside the parenthesis:
color(red)(2)(9 - x) > 4x + 92(9−x)>4x+9
(color(red)(2) xx 9) - (color(red)(2) xx x) > 4x + 9(2×9)−(2×x)>4x+9
18 - 2x > 4x + 918−2x>4x+9
Next, add color(red)(2x)2x and subtract color(blue)(9)9 from each side of the inequality to isolate the xx term while keeping the inequality balanced:
18 - color(blue)(9) - 2x + color(red)(2x) > 4x + color(red)(2x) + 9 - color(blue)(9)18−9−2x+2x>4x+2x+9−9
9 - 0 > (4 + color(red)(2))x + 09−0>(4+2)x+0
9 > 6x9>6x
Now, divide each side of the inequality by color(red)(6)6 to solve for xx while keeping the inequality balanced:
9/color(red)(6) > (6x)/color(red)(6)96>6x6
(3 xx 3)/color(red)(3 xx 2) > (color(red)(cancel(color(black)(6)))x)/cancel(color(red)(6))
(color(red)(cancel(color(black)(3))) xx 3)/color(red)(color(black)(cancel(color(red)(3))) xx 2) > x
3/2 > x
We can reverse or "flip: the entire inequality to state the solution in terms of x:
x < 3/2
