How do you solve #6> -5t-4# and graph the solution?

1 Answer
smendyka
Jan 9, 2018

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:

#6 + color(red)(4) > -5t - 4 + color(red)(4)#

#10 > -5t - 0#

#10 > -5t#

Now, divide each side of the inequality by #color(blue)(-5)# 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:

#10/color(blue)(-5) color(red)(<) (-5t)/color(blue)(-5)#

#-2 color(red)(<) (color(red)(cancel(color(black)(-5)))t)/cancel(color(blue)(-5))#

#-2 color(red)(<) t#

We can reverse or flip the entire inequality to state the solution in terms of #t#:

#t > -2#

To graph this we will draw a vertical line at #-2# on the horizontal axis.

The line will be a dashed line because the inequality operator does not contain an "or equal to" clause.

We will shade to the right side of the line because the inequality operator does contain a "greater than" clause:

graph{x > -2 [-10, 10, -5, 5]}

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