A compound inequality is an inequality that consists of multiple different inequalities put together. For example, the compound inequality states that is less than or equal to , or greater than .
For the compound "or" inequality to be satisfied, at least one of the separate inequalities must be satisfied. To illustrate:
satisfies the inequality because it satisfies
satisfies the inequality because it satisfies
does not satisfy the inequality because it does not satisfy and it also does not satisfy
To graph a compound inequality involving the word "or," we graph the two separate inequalities on the same number line. In this particular case,
the inequality consists of a closed circle at and an arrow to the left, while
the inequality consists of an open circle at and an arrow to the right.
The resulting graph is as follows:
Represent the inequality or on a number line.
The inequality or means that can take any value less than or greater than or equal to
To represent this on a number line, we graph the two separate inequalities:
the inequality consists of an open circle at and an arrow to the left.
the inequality consists of a closed circle at and an arrow to the right.
The resulting graph is as follows:
Which of the following number lines represents the inequality $x \leq 0$ or $x \geq 3?$
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Which of the following number lines represents the inequality $x \leq -1$ or $x > 0?$
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Which inequality corresponds to the highlighted region shown on the number line above?
The red rays contain all values less than or greater than In addition,
the open circle at implies that cannot be equal to and
the closed circle at implies that can be equal to
Therefore, the highlighted region represents or
Which inequality corresponds to the highlighted region shown on the number line above?
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a
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$x \leq 0$ or $ x > 2$ |
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b
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$x \leq 2$ or $ x \geq 0$ |
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$x < 2$ or $ x > 0$ |
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d
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$x < 0$ or $ x > 2$ |
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e
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$x \leq 0$ or $ x \leq 2$ |
Which inequality corresponds to the highlighted region shown on the number line above?
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$x < -3$ or $ x \geq 0$ |
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b
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$x < -3$ or $ x \leq 0$ |
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$x \leq -3$ or $ x < 0$ |
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d
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$x < -3$ or $ x < 0$ |
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e
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$x \leq -3$ or $ x \geq 0$ |
Which inequality corresponds to the highlighted region shown on the number line above?
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a
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$x < -1$ or $ x \geq 2$ |
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b
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$-1 \leq x < 2$ |
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$-1 < x \leq 2$ |
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d
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$x \leq -1$ or $ x > 2$ |
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e
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$x \leq -1$ or $ x \geq 2$ |
Compound inequalities can also be written with the word "and." However, such inequalities are often written together as a single expression with two inequality signs. For example, the compound inequality means that and
For the compound "and" inequality to be satisfied, both of the separate inequalities must be satisfied. To illustrate:
satisfies the inequality because it satisfies both and
does not satisfy the inequality because it does not satisfy
does not satisfy the inequality because it does not satisfy
To graph this compound inequality, we first graph the two inequalities separately.
Then, we keep only where they overlap.
Note: Any compound "and" inequality will always represent a segment between two points. So, it is not always necessary to draw both inequalities and find the overlap. To speed up the process, we can just draw the endpoints with open or closed circles as appropriate, and highlight the area between the endpoints.
What inequality corresponds to the highlighted region shown on the number line above?
The red segment contains all values between and In addition,
the closed circle at implies that can be equal to while
the open circle at implies that cannot be equal to
Therefore, the highlighted region represents
Which of the following number lines represents the inequality $2 < x < 5?$
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How is the inequality $-2 \leq x < 2$ represented on a number line?
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Which of the following number lines represents the inequality $1 \leq x \leq 3?$
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b
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Which inequality corresponds to the highlighted region shown on the number line above?
The red segment contains all values between and In addition,
the closed circle at implies that can be equal to while
the closed circle at implies that can be equal to
Therefore, the highlighted region represents
Which inequality corresponds to the highlighted region shown on the number line above?
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$ -2 \leq x \leq 1$ |
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b
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$x < -2$ or $x \geq 1$ |
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$- 2 \leq x < 1$ |
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d
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$-2 < x \leq 2$ |
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$-2 < x < 1$ |
Which inequality corresponds to the highlighted region shown on the number line above?
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$-1 < x < 2$ |
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$-1 < x \leq 2$ |
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$-1 \leq x \leq 2$ |
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$-2 \leq x < 1$ |
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$-1 \leq x < 2$ |