How do you solve and graph -6(w + 1) < 2(w + 5) ?

1 Answer
Jul 21, 2018

w > -2

Explanation:

-6(w+1) < 2(w+5)

Simplify each side by distributing:
-6w - 6 < 2w + 10

Add color(blue)(6w) to both sides of the inequality:
-6w - 6 quadcolor(blue)(+quad6w) < 2w + 10 quadcolor(blue)(+quad6w)

-6 < 8w + 10

Subtract color(blue)10 from both sides:
-6 quadcolor(blue)(-quad10) < 8w + 10 quadcolor(blue)(-quad10)

-16 < 8w

Divide both sides by color(blue)8:
(-16)/color(blue)8 < (8w)/color(blue)8

-2 < w

w > -2

This can be said as "w is greater than -2."

Here's a graph of it on a number line:
enter image source here
(mathwarehouse.com)

The open circle means that -2 is not one of the solutions.

Hope this helps!