Question

solve the inequality and graph the solution.
1 > \\(\frac{d}{-1}\\) - 2
plot the endpoints. select an endpoint to change it from closed to open. select the middle of the segment, ray, or line to delete it.
<---(-5)---(-4)---(-3)---(-2)---(-1)---(0)---(1)---(2)---(3)---(4)---(5)--->

Explanation:

Step1: Simplify the inequality

First, simplify \(\frac{d}{-1}\) to \(-d\), so the inequality becomes \(1 > -d - 2\).

Step2: Add 2 to both sides

Add 2 to both sides of the inequality: \(1 + 2> -d - 2 + 2\), which simplifies to \(3 > -d\).

Step3: Multiply both sides by -1 (and reverse inequality)

Multiply both sides by -1. Remember that when multiplying or dividing an inequality by a negative number, the direction of the inequality sign reverses. So we get \(-3 < d\) (or \(d > - 3\)).

Answer:

The solution to the inequality \(1>\frac{d}{-1}-2\) is \(d > - 3\). To graph this, we draw an open circle at \(d=-3\) (since the inequality is strict, \(d
eq - 3\)) and draw a ray to the right of \(-3\) on the number line.