How do you solve #-8t - 4\leq 12#?

1 Answer
smendyka
Dec 18, 2017

See a solution process below:

Explanation:

First, add #color(red)(4)# to each side of the inequality to isolate the #t# term while keeping the inequality balanced:

#-8t - 4 + color(red)(4) <= 12 + color(red)(4)#

#-8t - 0 <= 16#

#-8t <= 16#

Now, divide each side of the inequality by #color(blue)(-8)# to solve for #t# while keeping the inequality balanced. However, because we are multiplying or dividing an inequality by a negative number we must reverse the inequality operator:

#(-8t)/color(blue)(-8) color(red)(>=) 16/color(blue)(-8)#

#(color(blue)(cancel(color(black)(-8)))t)/cancel(color(blue)(-8)) color(red)(>=) -2#

#t >= -2#

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