What is the solution to the inequality #-6(4-x) <= -4(x+1)#?

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Answer 1 · 2015-08-31T22:35:32

#x <=2#

Use the distributive property of multiplcation to expand the parantheses

#-6 * 4 - 6 * (-x) <= -4 * x -4 * 1#

#-24 + 6x <= -4x - 4#

Rearrange the inequality to get a single #x#-term on one side

#6x + 4x <= -4 + 24#

#10x <= 20#

This is equivalent to

#x <= 2#

So, for any value of #x# that is smaller than or equal to #2#, the inequality will be true. The solution set will thus be #(-oo, 2]#.