How do you solve and graph #-t/5+7> -4#?

To solve, first, subtract #color(red)(7)# from each side of the inequality to isolate the #t# term while keeping the inequality balanced:

#-t/5 + 7 - color(red)(7) > -4 - color(red)(7)#

#-t/5 + 0 > -11#

#-t/5 > -11#

Now, multiply 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:

#color(blue)(-5) xx -t/5 color(red)(<) color(blue)(-5) xx -11#

#(color(blue)(-5)t)/-5 color(red)(<) 55#

#t color(red)(<) 55#

To graph this we draw a vertical line at #55# on the horizontal axis.

The line will be dashed because the inequality operator DOES NOT contain an "or equal to"clause.

We will shade to the left of the line because the operator is a "less" inequality:

graph{x<55 [-80, 80, -40, 40]}

Solve and graph:

#-t/5+7> -4#

Subtract #7# from both sides.

#-t/5> -4-11#

Simplify.

#-t/5> -11#

Multiple both sides by #5#.

#-t> -55#

Multiply both sides by #-1#. This will reverse the inequality.

#t<55#

Number line

Since this is an equality only, a circle is drawn around the number #55# and then the number line goes to the left to infinity, which is represented by the left-facing arrow.

Graph

The graph is a dashed vertical line at #x=55#, which goes to infinity. The dashed line means that #55# is not a part of the inequality. The area to the left of #x=55# is shaded in on the left side to indicate that #t<55# and it will go on to infinity.

graph{x<55 [30.91, 66.94, -7.58, 10.44]}