Write the inequality in interval notation. Then graph the interval. x <= - 1 or x > 3
Interval notation: (-∞, -1] U (3, ∞)
Graph:
______________-1-----3___________________
To write the inequality in interval notation, we can break it down into two separate inequalities:
1. x <= -1
2. x > 3
The first inequality, x <= -1, includes all real numbers less than or equal to -1. This can be represented in interval notation as (-∞, -1].
The second inequality, x > 3, includes all real numbers greater than 3. This can be represented in interval notation as (3, ∞).
To graph the interval, we can plot these two intervals on a number line:
On the number line, we mark a closed circle at -1 and shade the line to the left. This represents the first interval (-∞, -1].
Then, we mark an open circle at 3 and shade the line to the right. This represents the second interval (3, ∞).
The resulting graph will have an open circle at 3 on the number line, shaded to the right, and a closed circle at -1 on the number line, shaded to the left.
To write the inequality x <= -1 or x > 3 in interval notation, we first need to separate it into two separate inequalities:
1) x <= -1, and
2) x > 3.
For the first inequality, x <= -1, the interval notation can be written as (-∞, -1] since it includes -1 and all values that are less than or equal to -1.
For the second inequality, x > 3, the interval notation can be written as (3, ∞) since it includes 3 and all values greater than 3.
Now, to graph the interval, we can represent it on a number line. Here is how the graph would look:
-∞ .............. -1 [ 3 ............. ∞)
The square bracket [ represents that -1 is included, and the round parenthesis ( indicates that 3 is not included in the interval.
The portion to the left of -1 and the portion to the right of 3 are shaded to show that they are part of the solution set.