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

Jan 9, 2018

See a solution process below:

Explanation:

First, add $\textcolor{red}{4}$ to each side of the inequality to isolate the $t$ term while keeping the inequality balanced:

$6 + \textcolor{red}{4} > - 5 t - 4 + \textcolor{red}{4}$

$10 > - 5 t - 0$

$10 > - 5 t$

Now, divide each side of the inequality by $\textcolor{b l u e}{- 5}$ 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:

$\frac{10}{\textcolor{b l u e}{- 5}} \textcolor{red}{<} \frac{- 5 t}{\textcolor{b l u e}{- 5}}$

$- 2 \textcolor{red}{<} \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 5}}} t}{\cancel{\textcolor{b l u e}{- 5}}}$

$- 2 \textcolor{red}{<} t$

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]}