Question

solve the inequally t-5≤-7 and graph the solution

Answer 1

We have to solve the inequality

$t-5\leq-7$

To do that, we add the 5 to both sides of the inequality, then we have

$\begin{gathered} t-5\leq-7 \\ t-5+5\leq-7+5 \\ t\leq-2 \end{gathered}$

Then the solution to the inequality in interval notation is

$(-\infty,-2\rbrack$

To graph the inequality we first graph the equation

$t-5=-7$

simplifying the equation we have

$t=-2$

This represents a vertical line that intersects with -2

Now we have to decide wich of the two semiplanes we have to choose to "color" that represents the solution of the inequality, since the solution was

$t\leq-2$

we color the semiplane to the left of the line