Math

QuestionIdentify the graph for the inequalities x8>0\frac{x}{8}>0 or 4x32-4 x \geq 32.

Studdy Solution

STEP 1

Assumptions1. We are dealing with two inequalities x8>0\frac{x}{8}>0 and 4x32-4x \geq32 . We are looking for the graph that represents the solution to either of these inequalities3. The inequalities are linear, so they will be represented by straight lines on the graph

STEP 2

First, let's solve the inequality x8>0\frac{x}{8}>0 for xx.
To do this, we multiply both sides of the inequality by8.
x>0×8x >0 \times8

STEP 3

implify the inequality.
x>0x >0This means that for the inequality x8>0\frac{x}{8}>0, any xx value greater than0 is a solution.

STEP 4

Next, let's solve the inequality 4x32-4x \geq32 for xx.
To do this, we divide both sides of the inequality by -4. Remember, when we divide or multiply an inequality by a negative number, the direction of the inequality sign changes.
x324x \leq \frac{32}{-4}

STEP 5

implify the inequality.
x8x \leq -8This means that for the inequality 4x32-4x \geq32, any xx value less than or equal to -8 is a solution.

STEP 6

Now, let's graph these inequalities.
For x8>0\frac{x}{8}>0, we have a ray starting at0 and extending to the right, not including0.
For 4x32-4x \geq32, we have a ray starting at -8 and extending to the left, including -8.
The graph that represents these inequalities is a number line with a closed circle at -8, an open circle at0, a ray extending to the left from -8, and a ray extending to the right from0.

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