Question

Solve for x and graph the solution on the number line below.


−2≥x+3or
7≤x+3
Answer
open or closed
Answer
so are they closed or open
Answer
put this on a number line
Answer
closed or open
Answered by GPT 3.5
To solve for x, we'll solve each inequality separately and then graph the solutions on a number line.

For the first inequality:
-2 ≥ x + 3

Subtract 3 from both sides:
-2 - 3 ≥ x
-5 ≥ x

So the solution for the first inequality is x ≤ -5.

Now for the second inequality:
7 ≤ x + 3

Subtract 3 from both sides:
7 - 3 ≤ x
4 ≤ x

So the solution for the second inequality is x ≥ 4.

Now let's graph the solutions on a number line:

<---------------------|---------------------|--------------------->
-5 4

The solution for the first inequality, x ≤ -5, includes all numbers less than or equal to -5. So we shade to the left of -5 on the number line.

The solution for the second inequality, x ≥ 4, includes all numbers greater than or equal to 4. So we shade to the right of 4 on the number line.

Combining the shaded regions, the solution for both inequalities is the overlap between the two shaded regions. So the solution is x ≤ -5 or x ≥ 4.

<---------------------|---------------------|--------------------->
-5 4

The shaded regions represent the solution for x.
Answered by GPT 3.5
Both inequalities are not inclusive of the boundary points -5 and 4 since there is a strict inequality. Therefore, the solution should be represented as (-∞, -5) U (4, ∞), where the parentheses indicate an open interval.
Answered by GPT 3.5
Both inequalities are open, since the boundary points are not included in the solution.
Answered by GPT 3.5
Sure! Here is the solution on a number line:

<--------------o-----o---------------o---------->
-∞ -5 4 +∞

The circle on -5 and 4 indicates that these points are not included in the solution, making the intervals open. The line to the left of -5 and the line to the right of 4 are not shaded, representing the open intervals (-∞, -5) and (4, +∞) respectively.
Answered by GPT 3.5
I apologize for the confusion. The correct representation should be:

<==============o-----o--------------o============>
-∞ -5 4 +∞

The filled-in circles on -5 and 4 indicate that these points are included in the solution, making the intervals closed. The line to the left of -5 and the line to the right of 4 are shaded, representing the closed intervals [-∞, -5] and [4, +∞] respectively.