Question

solve the inequality for x.
30 - 5x < 6 - 9x
simplify your answer as much as possible.

Explanation:

Step1: Add 9x to both sides

To isolate the x - terms on one side, we add 9x to both sides of the inequality \(30 - 5x<6 - 9x\).
Using the addition property of inequalities (adding the same number to both sides of an inequality does not change the direction of the inequality), we get:
\(30 - 5x+9x<6 - 9x + 9x\)
Simplifying the left - hand side (\(-5x + 9x=4x\)) and the right - hand side (\(-9x+9x = 0\)), the inequality becomes \(30 + 4x<6\).

Step2: Subtract 30 from both sides

Now, we want to isolate the term with x. We subtract 30 from both sides of the inequality \(30 + 4x<6\).
Using the subtraction property of inequalities (subtracting the same number from both sides of an inequality does not change the direction of the inequality), we have:
\(30 + 4x-30<6 - 30\)
Simplifying the left - hand side (\(30-30 = 0\)) and the right - hand side (\(6 - 30=-24\)), the inequality becomes \(4x<-24\).

Step3: Divide both sides by 4

To solve for x, we divide both sides of the inequality \(4x<-24\) by 4.
Since 4 is a positive number, the direction of the inequality sign remains the same.
\(\frac{4x}{4}<\frac{-24}{4}\)
Simplifying, we get \(x < - 6\).

Answer:

\(x < - 6\)