How do you solve #-5r + 6\leq - 5( r + 2)#?

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Answer 1 · 2017-04-29T01:43:19

See the solution process below:

First, expand the terms in parenthesis on the right side of the inequality:

#-5r + 6 <= (-5 * r) - (5 * 2)#

#-5r + 6 <= -5r - 10#

Now, add #color(red)(5r)# to each side of the inequality to eliminate the variable:

#color(red)(5r) - 5r + 6 <= color(red)(5r) - 5r - 10#

#0 + 6 <= 0 - 10#

#6 <= -10#

However, #6# IS NOT LESS THAN OR EQUAL TO #-10#, therefore there is no solution to this problem.

Or, the solution is the empty or null set: #{O/}#