First, expand the terms in parenthesis on each side of the inequality by multiplying each term within the parenthesis by the term outside the parenthesis:
color(red)(-4)(x + 6) - 9 > color(blue)(2)(x - 9)−4(x+6)−9>2(x−9)
(color(red)(-4) * x) + (color(red)(-4) * 6) - 9 > (color(blue)(2) * x) - (color(blue)(2) * 9)(−4⋅x)+(−4⋅6)−9>(2⋅x)−(2⋅9)
-4x - 24 - 9 > 2x - 18−4x−24−9>2x−18
-4x - 33 > 2x - 18−4x−33>2x−18
Now, add color(red)(4x)4x and color(blue)(18)18 to each side of the inequality to isolate the xx term while keeping the inequality balanced:
color(red)(4x) - 4x - 33 + color(blue)(18) > color(red)(4x) + 2x - 18 + color(blue)(18)4x−4x−33+18>4x+2x−18+18
0 - 15 > (color(red)(4) + 2)x - 00−15>(4+2)x−0
-15 > 6x−15>6x
Now, divide each side of the inequality by color(red)(6)6 to solve for xx while keeping the inequality balanced:
-15/color(red)(6) > (6x)/color(red)(6)−156>6x6
-(3 xx 5)/color(red)(3 xx 2) > (color(red)(cancel(color(black)(6)))x)/cancel(color(red)(6))
-(color(red)(cancel(color(black)(3))) xx 5)/color(red)(color(black)(cancel(color(red)(3))) xx 2) > x
-5/2 > x
To state the solution in terms of x we can reverse or "flip" the entire inequality:
x < -5/2
