2.
If 4 SX 5 9 then which of the following is
true?
(A) (x-4) (X - 9) <0
(B) (x-4) (x - 9) > 0
(C) (x-4) (x-9) SO
(D) (x-4) (x-9) 2 0
Answers
Answer:
Simplifying
(x + -4)(x + 9) = 0
Reorder the terms:
(-4 + x)(x + 9) = 0
Reorder the terms:
(-4 + x)(9 + x) = 0
Multiply (-4 + x) * (9 + x)
(-4(9 + x) + x(9 + x)) = 0
((9 * -4 + x * -4) + x(9 + x)) = 0
((-36 + -4x) + x(9 + x)) = 0
(-36 + -4x + (9 * x + x * x)) = 0
(-36 + -4x + (9x + x2)) = 0
Combine like terms: -4x + 9x = 5x
(-36 + 5x + x2) = 0
Solving
-36 + 5x + x2 = 0
Solving for variable 'x'.
Factor a trinomial.
(-9 + -1x)(4 + -1x) = 0
Subproblem 1
Set the factor '(-9 + -1x)' equal to zero and attempt to solve:
Simplifying
-9 + -1x = 0
Solving
-9 + -1x = 0
Move all terms containing x to the left, all other terms to the right.
Add '9' to each side of the equation.
-9 + 9 + -1x = 0 + 9
Combine like terms: -9 + 9 = 0
0 + -1x = 0 + 9
-1x = 0 + 9
Combine like terms: 0 + 9 = 9
-1x = 9
Divide each side by '-1'.
x = -9
Simplifying
x = -9
Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:
Simplifying
4 + -1x = 0
Solving
4 + -1x = 0
Move all terms containing x to the left, all other terms to the right.
Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4
Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4
Combine like terms: 0 + -4 = -4
-1x = -4
Divide each side by '-1'.
x = 4
Simplifying
x = 4
Solution
x = {-9, 4}