Math  /  Algebra

QuestionGraph the solution to this inequality on the number line. x+5<2x+5<-2
First, select the correct ray. Then, select the location of the endpoint to plot the inequality on the number line.

Studdy Solution

STEP 1

1. We are given the inequality x+5<2 x + 5 < -2 .
2. We need to solve the inequality for x x .
3. We will graph the solution on a number line.

STEP 2

1. Solve the inequality for x x .
2. Determine the type of ray and endpoint for the graph.
3. Plot the solution on the number line.

STEP 3

Start by isolating x x in the inequality x+5<2 x + 5 < -2 .
Subtract 5 from both sides:
x+55<25 x + 5 - 5 < -2 - 5
Simplify:
x<7 x < -7

STEP 4

The inequality x<7 x < -7 indicates that x x is less than 7-7.
This means the ray will point to the left on the number line.
The endpoint at 7-7 will be an open circle because the inequality is strict (i.e., it does not include 7-7).

STEP 5

To graph the solution on the number line:
1. Draw a number line.
2. Locate the point 7-7 on the number line.
3. Place an open circle at 7-7 to indicate that 7-7 is not included in the solution.
4. Draw a ray extending to the left from the open circle to represent all numbers less than 7-7.

The solution is graphed as a ray pointing left from an open circle at 7-7 on the number line.

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