What value of x is in the solution set of the inequality 9(2x + 1) < 9x – 18?
A. –4
B. –3
C. –2
D. –1
Answer (2)
The solution to the inequality 9 ( 2 x + 1 ) < 9 x − 18 is x < − 3 . Values less than -3, such as -4, are included in the solution set.
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To solve the inequality 9 ( 2 x + 1 ) < 9 x − 18 , follow these steps:
Distribute the 9 on the left side :
9 × 2 x + 9 × 1 = 18 x + 9 So the inequality becomes: 18 x + 9 < 9 x − 18
Get all the terms involving x on one side and constant terms on the other side :
Subtract 9 x from both sides:
18 x + 9 − 9 x < 9 x − 18 − 9 x Simplifying gives: 9 x + 9 < − 18
Subtract 9 from both sides to isolate the term with x :
9 x + 9 − 9 < − 18 − 9 This results in: 9 x < − 27
Divide each side by 9 to solve for x :
x < 9 − 27 Simplifying gives: x < − 3
Therefore, the value of x that fits in the solution set is x = − 4 since − 4 < − 3 . Thus, the correct multiple choice option is − 4 .
