QuestionExpress the inequality $x < -6$ or $x > -2$ in interval notation.

Studdy Solution

STEP 1

Assumptions1. The inequality is given as $x < -6$ or $x > -$ . . We need to express this inequality in interval notation.

STEP 2

Interval notation is a way of expressing the solution set of an inequality. It uses parentheses and brackets to indicate whether the endpoints are included in the interval. Parentheses are used when the endpoint is not included, and brackets are used when the endpoint is included.

STEP 3

For the inequality $x < -6$ , since $x$ is strictly less than -6, -6 is not included in the interval. So, we use a parenthesis for -6. The interval extends to negative infinity. In interval notation, negative infinity is always represented with a parenthesis.

STEP 4

The interval notation for $x < -6$ is $(-∞, -6)$ .

STEP 5

For the inequality $x > -2$ , since $x$ is strictly greater than -2, -2 is not included in the interval. So, we use a parenthesis for -2. The interval extends to positive infinity. In interval notation, positive infinity is always represented with a parenthesis.

STEP 6

The interval notation for $x > -2$ is $(-2, ∞)$ .

STEP 7

Since the original inequality is an "or" inequality, we combine the two intervals using the union symbol, which is denoted by "".

STEP 8

The interval notation for the given inequality is $(-∞, -6) \cup (-2, ∞)$ .
This means that the solution to the inequality is all numbers less than -6 or greater than -2.

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QuestionExpress the inequality $x < -6$ or $x > -2$ in interval notation.

Studdy Solution

STEP 1

Assumptions1. The inequality is given as $x < -6$ or $x > -$ . . We need to express this inequality in interval notation.

STEP 2

Interval notation is a way of expressing the solution set of an inequality. It uses parentheses and brackets to indicate whether the endpoints are included in the interval. Parentheses are used when the endpoint is not included, and brackets are used when the endpoint is included.

STEP 3

For the inequality $x < -6$ , since $x$ is strictly less than -6, -6 is not included in the interval. So, we use a parenthesis for -6. The interval extends to negative infinity. In interval notation, negative infinity is always represented with a parenthesis.

STEP 4

The interval notation for $x < -6$ is $(-∞, -6)$ .

STEP 5

For the inequality $x > -2$ , since $x$ is strictly greater than -2, -2 is not included in the interval. So, we use a parenthesis for -2. The interval extends to positive infinity. In interval notation, positive infinity is always represented with a parenthesis.

STEP 6

The interval notation for $x > -2$ is $(-2, ∞)$ .

STEP 7

Since the original inequality is an "or" inequality, we combine the two intervals using the union symbol, which is denoted by "".

STEP 8

The interval notation for the given inequality is $(-∞, -6) \cup (-2, ∞)$ .
This means that the solution to the inequality is all numbers less than -6 or greater than -2.

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QuestionExpress the inequality x<−6x < -6x<−6 or x>−2x > -2x>−2 in interval notation.

Studdy Solution

STEP 1

Assumptions1. The inequality is given as x<−6x < -6x<−6 or x>−x > -x>−. . We need to express this inequality in interval notation.

STEP 2

Interval notation is a way of expressing the solution set of an inequality. It uses parentheses and brackets to indicate whether the endpoints are included in the interval. Parentheses are used when the endpoint is not included, and brackets are used when the endpoint is included.

STEP 3

For the inequality x<−6x < -6x<−6, since xxx is strictly less than -6, -6 is not included in the interval. So, we use a parenthesis for -6. The interval extends to negative infinity. In interval notation, negative infinity is always represented with a parenthesis.

STEP 4

The interval notation for x<−6x < -6x<−6 is (−∞,−6)(-∞, -6)(−∞,−6).

STEP 5

For the inequality x>−2x > -2x>−2, since xxx is strictly greater than -2, -2 is not included in the interval. So, we use a parenthesis for -2. The interval extends to positive infinity. In interval notation, positive infinity is always represented with a parenthesis.

STEP 6

The interval notation for x>−2x > -2x>−2 is (−2,∞)(-2, ∞)(−2,∞).

STEP 7

Since the original inequality is an "or" inequality, we combine the two intervals using the union symbol, which is denoted by "".

STEP 8

The interval notation for the given inequality is (−∞,−6)∪(−2,∞)(-∞, -6) \cup (-2, ∞)(−∞,−6)∪(−2,∞).This means that the solution to the inequality is all numbers less than -6 or greater than -2.

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QuestionExpress the inequality $x < -6$ or $x > -2$ in interval notation.

Assumptions1. The inequality is given as $x < -6$ or $x > -$ . . We need to express this inequality in interval notation.

For the inequality $x < -6$ , since $x$ is strictly less than -6, -6 is not included in the interval. So, we use a parenthesis for -6. The interval extends to negative infinity. In interval notation, negative infinity is always represented with a parenthesis.

The interval notation for $x < -6$ is $(-∞, -6)$ .

For the inequality $x > -2$ , since $x$ is strictly greater than -2, -2 is not included in the interval. So, we use a parenthesis for -2. The interval extends to positive infinity. In interval notation, positive infinity is always represented with a parenthesis.

The interval notation for $x > -2$ is $(-2, ∞)$ .

The interval notation for the given inequality is $(-∞, -6) \cup (-2, ∞)$ .
This means that the solution to the inequality is all numbers less than -6 or greater than -2.