Question

what value of x is in the solution set of the inequality $9(2x + 1) < 9x - 18$?
-4
-3
-2
-1

Explanation:

Step1: Expand the left side

First, we expand \(9(2x + 1)\) using the distributive property \(a(b + c)=ab+ac\). So, \(9(2x + 1)=9\times2x+9\times1 = 18x+9\). The inequality becomes \(18x + 9<9x-18\).

Step2: Subtract \(9x\) from both sides

Subtract \(9x\) from both sides of the inequality to get all \(x\) terms on one side. \((18x + 9)-9x<(9x - 18)-9x\), which simplifies to \(9x+9<-18\).

Step3: Subtract 9 from both sides

Subtract 9 from both sides: \((9x + 9)-9< - 18-9\), so \(9x<-27\).

Step4: Divide by 9

Divide both sides by 9 (since 9 is positive, the inequality sign remains the same): \(\frac{9x}{9}<\frac{-27}{9}\), which gives \(x < - 3\).

Now we check the options:

• For \(x=-4\): \(-4<-3\), so it satisfies \(x < - 3\).
• For \(x = - 3\): \(-3\) is not less than \(-3\), so it does not satisfy.
• For \(x=-2\): \(-2>-3\), does not satisfy.
• For \(x = - 1\): \(-1>-3\), does not satisfy.

Answer:

A. \(-4\)