Question

linear inequalities (level 2)
question
solve the following inequality for w. write your answer in simplest form.
-1 - (-6w - 10) < -7w - 8 - 2w

Explanation:

Step1: Simplify both sides

First, simplify the left - hand side: \(-1-(-6w - 10)=-1 + 6w+10=6w + 9\)
Then, simplify the right - hand side: \(-7w-8 - 2w=-9w-8\)
So the inequality becomes \(6w + 9<-9w-8\)

Step2: Add \(9w\) to both sides

To get all the \(w\) terms on one side, add \(9w\) to both sides of the inequality:
\(6w+9w + 9<-9w + 9w-8\)
\(15w+9<-8\)

Step3: Subtract 9 from both sides

Subtract 9 from both sides to isolate the term with \(w\):
\(15w+9 - 9<-8 - 9\)
\(15w<-17\)

Step4: Divide both sides by 15

Divide both sides of the inequality by 15. Since 15 is positive, the direction of the inequality sign remains the same:
\(w<-\frac{17}{15}\)

Answer:

\(w<-\frac{17}{15}\)