Question

1. solve 2 + 5(-w + 3) > 2w + 8 - 8w

inequality notation:
interval notation:

Explanation:

Step1: Expand both sides

First, expand the left - hand side: \(2 + 5(-w + 3)=2-5w + 15=-5w+17\)
Then, simplify the right - hand side: \(2w + 8-8w=-6w + 8\)
So the inequality becomes \(-5w + 17>-6w + 8\)

Step2: Add \(6w\) to both sides

To get all the \(w\) terms on one side, add \(6w\) to both sides of the inequality:
\(-5w+6w + 17>-6w + 6w+8\)
Simplify: \(w + 17>8\)

Step3: Subtract 17 from both sides

Subtract 17 from both sides to solve for \(w\):
\(w+17 - 17>8 - 17\)
Simplify: \(w>-9\)

Inequality Notation Answer:

\(w > - 9\)

Interval Notation Answer:

\((-9,\infty)\)

Answer:

Step1: Expand both sides

First, expand the left - hand side: \(2 + 5(-w + 3)=2-5w + 15=-5w+17\)
Then, simplify the right - hand side: \(2w + 8-8w=-6w + 8\)
So the inequality becomes \(-5w + 17>-6w + 8\)

Step2: Add \(6w\) to both sides

To get all the \(w\) terms on one side, add \(6w\) to both sides of the inequality:
\(-5w+6w + 17>-6w + 6w+8\)
Simplify: \(w + 17>8\)

Step3: Subtract 17 from both sides

Subtract 17 from both sides to solve for \(w\):
\(w+17 - 17>8 - 17\)
Simplify: \(w>-9\)

Inequality Notation Answer:

\(w > - 9\)

Interval Notation Answer:

\((-9,\infty)\)