How do you solve #-25x - 15\leq - 20x - 7#?

3 Answers
Jul 15, 2018

Work backwards, always doing the opposite combine like and watch the negative signs

Explanation:

The goal is to get x a lost number by itself on one side of the inequality. When something is lost it is best to work backwards from the last place it was known to be. x is an unknown so use the same principle.

Jul 15, 2018

#x >=-8/5#

Explanation:

Treat an inequality in the same way as an equation, unless you multiply or divide by a negative number, in which case the inequality sign changes around.

Therefore try to keep the #x# term positive to avoid the problem.

#-25x-15 <= -20x-7#

Add #25x# to both sides:

#cancel(-25x)-15cancel(+25x) <= -20x-7+25x#

Add #7# to both sides

#-15+7 <=5xcancel(-7)+cancel(7)#

#-8 <= 5x#

#(-8)/5 <=x#

#x >=-8/5#

Jul 15, 2018

#x>=-8/5#

Explanation:

For the most part, we can treat this like a linear equation. Let's add #20x# to both sides to get

#-5x-15<=-7#

Next, add #15# to both sides to isolate the #x# term:

#-5x<=8#

Lastly, we can divide both sides by #-5#. However, since we divided by a negative, we flip the direction of the inequality.

We now have

#x>=-8/5#

Hope this helps!