Question

solve the inequality and graph the solution.
$3 > \frac{t}{-1} - 5$
to draw a ray, plot an endpoint and select an arrow. select an endpoint to change it from closed to open. select the middle of the ray to delete it.
-10 -8 -6 -4 -2 0 2 4 6 8 10

Explanation:

Step1: Simplify the inequality

First, simplify \(\frac{t}{-1}\) to \(-t\). So the inequality becomes \(3 > -t - 5\).

Step2: Add 5 to both sides

Add 5 to each side of the inequality: \(3 + 5 > -t - 5 + 5\), which simplifies to \(8 > -t\).

Step3: Multiply by -1 (reverse inequality)

Multiply both sides by -1. Remember, when multiplying or dividing an inequality by a negative number, the inequality sign flips. So we get \(-8 < t\) (or \(t > -8\)).

Answer:

The solution to the inequality is \(t > -8\). To graph this, plot an open circle at \(-8\) (since the inequality is strict, \(t
eq -8\)) and draw an arrow to the right (indicating all values greater than \(-8\)).