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Math  /  Algebra

QuestionQuestion 8, 1.7.1-10 Points: 0 of 1
Match each inequality below with its equivalent interval notation.
1. x<−2x<-2
2. x≤2x \leq 2
3. −6<x≤2-6<x \leq 2
4. x2≥0x^{2} \geq 0
5. x≥−2x \geq-2
6. 2≤x2 \leq \mathrm{x} 7. 8. 9. (−∞,∞)(-\infty, \infty) [−2,∞)[-2, \infty) (−∞,2](-\infty, 2] (−∞,−2](-\infty,-2] (−6,2](-6,2] [2,∞)[2, \infty) (−∞,−2)(-\infty,-2) (0,7)(0,7) [−6,2)[-6,2) (−∞,−6)∪(2,∞)(-\infty,-6) \cup(2, \infty)
Drag the equivalent interval notation above to the matching inequality below. 1. 9. 2. □\square 10. □\square
3. □\square 4. 4.
U
5. □\square 6.
7. □\square S

Studdy Solution

STEP 1

1. We are given a list of inequalities and a list of interval notations.
2. We need to match each inequality with its equivalent interval notation.
3. The inequalities and intervals are assumed to be in standard mathematical form.

STEP 2

1. Understand the inequality.
2. Convert the inequality to interval notation.
3. Match the converted interval with the given options.
4. Repeat for each inequality.

STEP 3

Understand the inequality x<−2 x < -2 .

STEP 4

Convert the inequality x<−2 x < -2 to interval notation. This represents all numbers less than −2-2, which is:
(−∞,−2) (-\infty, -2)

STEP 5

Match the interval (−∞,−2) (-\infty, -2) with the given options.

STEP 6

Understand the inequality x≤2 x \leq 2 .

STEP 7

Convert the inequality x≤2 x \leq 2 to interval notation. This represents all numbers less than or equal to 22, which is:
(−∞,2] (-\infty, 2]

STEP 8

Match the interval (−∞,2] (-\infty, 2] with the given options.

STEP 9

Understand the inequality −6<x≤2-6 < x \leq 2.

STEP 10

Convert the inequality −6<x≤2-6 < x \leq 2 to interval notation. This represents all numbers greater than −6-6 and less than or equal to 22, which is:
(−6,2] (-6, 2]

STEP 11

Match the interval (−6,2] (-6, 2] with the given options.

STEP 12

Understand the inequality x2≥0 x^2 \geq 0 .

STEP 13

Convert the inequality x2≥0 x^2 \geq 0 to interval notation. Since x2 x^2 is always non-negative for all real numbers, the interval is:
(−∞,∞) (-\infty, \infty)

STEP 14

Match the interval (−∞,∞) (-\infty, \infty) with the given options.

STEP 15

Understand the inequality x≥−2 x \geq -2 .

STEP 16

Convert the inequality x≥−2 x \geq -2 to interval notation. This represents all numbers greater than or equal to −2-2, which is:
[−2,∞) [-2, \infty)

STEP 17

Match the interval [−2,∞) [-2, \infty) with the given options.

STEP 18

Understand the inequality 2≤x 2 \leq x .

STEP 19

Convert the inequality 2≤x 2 \leq x to interval notation. This represents all numbers greater than or equal to 22, which is:
[2,∞) [2, \infty)

STEP 20

Match the interval [2,∞) [2, \infty) with the given options.
The matched intervals are:
1. x<−2 x < -2 matches with (−∞,−2) (-\infty, -2)
2. x≤2 x \leq 2 matches with (−∞,2] (-\infty, 2]
3. −6<x≤2 -6 < x \leq 2 matches with (−6,2] (-6, 2]
4. x2≥0 x^2 \geq 0 matches with (−∞,∞) (-\infty, \infty)
5. x≥−2 x \geq -2 matches with [−2,∞) [-2, \infty)
6. 2≤x 2 \leq x matches with [2,∞) [2, \infty)

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