How do you solve #5 - x > 2(x+1)#?

1 Answer
Aug 31, 2015

Answer:

#x in (-oo, 1)#

Explanation:

Your goal here is to isolate #x# on one side of the inequality. Start by suing the distributive property of multiplication to expand the paranthesis on the right-hand side

#5 -x > 2*x + 2 * 1#

Move #2x# on the left-hand side of the inequality, and #5# on the right-hand side of the inequality - do not forget to change their signs!

#-x - 2x > 2 - 5#

#-3x > -3#

Finally, divide both sides by #(-3)#, but keep in mind that you need to change the sign of the inequality as well

#(color(red)(cancel(color(black)(-3))) * x)/color(red)(cancel(color(black)(-3))) < ((-3))/((-3))#

#x < 1#

So, for any value of #x<1#, the inequality will be true. The solution set will thus be #x in (-oo, 1)#.