Question

Solve -4x - 5 > -9 and describe the graph of the solution.

x > 1; closed circle on 1, shading to the right

x < 1; closed circle on 1, shading to the left

x < 1; open circle on 1, shading to the left

x > 1; open circle on 1, shading to the right

Answer 1

x < 1; open circle on 1, shading to the left

Answer 2

are u sure this is right can anyone explain it

Answer 3

@pbking101
Here's a quick description of how to do these problems:

1) Turn the inequality into an equality and solve to find the endpoint.
\[-4x-5 > -9 \rightarrow -4x -5 = -9\]Add 5 to both sides\[-4x-5+5 = -9+5\]\[-4x=-4\]Divide both sides by -4 to isolate \(x\)\[x=1\]

So, we know that the solution has x = 1 as an endpoint.

2) Test a point near the solution to find the direction of shading.
We know that x = 1 is the endpoint. Let's try a point to the left at x = 0 (easy arithmetic!)
\[-4(0) -5 > -9\]\[-5 > -9\]That's true, so x = 0 is a point on the line that would be shaded. As it is to the left of our endpoint x = 1, we know the shading goes to the left.

For practice and an abundance of caution, let's also try a point to the right: x = 2
\[-4(2) -5 > -9\]\[-8 -5 > -9\]\[-13 > -9\]That's not true, so we know that x = 2 is not shaded and conclude that our decision to shade only to the left is correct.

3) Choose open or closed circle depending on inequality.
Open circle means the endpoint is not included, and is used if the inequality sign is one of \(\lt,\gt\). Closed circle means the endpoint is included, and is used if the inequality sign has an equals component: \(\le,\ge\).

We've got \(\gt\) in our inequality, so the endpoint is not included, and we use an open circle. Our answer is open circle at x = 1, shading to the left.