Question

Solve the following inequality for w then simplify
-w+9>6w+8

Answer 1

`\displaystyle (-\infty,(1)/(7))`

Explanation:

Inequalities

To solve the inequality:

`-w+9>6w+8`

We need to perform the required operations on both sides of the inequality to have the variable w isolated.

First, we subtract 9:

`-w+9>6w+8`

`-w>6w+8-9`

Subtracting 6w:

`-w-6w>+8-9`

Operating:

-7w>-1

Now we divide by -7 but recall that when dividing by a negative number, we must flip the inequality sign:

`\displaystyle w<(-1)/(-7)`

Operating:

`\displaystyle w<(1)/(7)`

Solution:

`\mathbf{\displaystyle (-\infty,(1)/(7))}`