What is the solution to the inequality -10.5 -7x> -4.510.57x>4.5?

1 Answer
May 18, 2016

x < -6/7x<67

Explanation:

Given,

-10.5-7x > -4.510.57x>4.5

Start by adding 10.510.5 to both sides.

-10.5color(white)(i)color(red)(+10.5)-7x > -4.5color(white)(i)color(red)(+10.5)10.5i+10.57x>4.5i+10.5

-7x > 67x>6

Divide both sides by -77.

color(red)((color(black)(-7x))/-7) > color(red)(color(black)6/-7)7x7>67

x > -6/7x>67

However, recall that you must always flip the inequality sign whenever you divide by a negative number. Thus,

color(green)(|bar(ul(color(white)(a/a)color(black)(x < -6/7)color(white)(a/a)|)))