Question

Match each inequality with the number line that represents it.

Answer 1

-3 ≤ x is the same as x ≥ -3 which is 2.
x ≥ 3 is 5.
x ≤ -3 is 4.
x < 3 is 1.
-3 > x is the same as x < -3 which is 3.

Answer 2

Answer:

1)  x<3

2) x≥3

3) x< -3

4) x≤ -3

5) x>3

6) x≥ -3

Step-by-step explanation:

We have to match each of the inequalities that is represented in the number line.

1)

The first number line covers the region all the real numbers which are less than 3.

Since, there is a open circle at 3.

so, the inequality is:

x<3

2)

The second number line covers all the real numbers that are greater than or equal to three since the region right to 3 is shaded and there is a closed circle at 3.

Hence, the region is:

[3,∞).

So, the region is:

x≥ 3.

3)

The third number line covers all the real numbers which are less than -3.

i.e. the region (-∞,-3)

Since there is a open circle at -3 so -3 is not included.

Hence, x< -3.

4)

The fourth number line covers all the real numbers that are less than or equal to minus three since the region left of -3  is shaded and there is a closed circle at -3.

Hence, the region is:

(-∞,-3]

So, the region is:

x≤-3.

5)

The second number line covers all the real numbers that are greater than  three since the region right to 3 is shaded and there is a open circle at 3.

Hence, the region is:

(3,∞).

So, the region is:

x> 3.

6)

The second number line covers all the real numbers that are greater than or equal to three since the region right to -3 is shaded and there is a closed circle at -3.

Hence, the region is:

[-3,∞).

So, the region is:

x≥ -3.