representation on number line

Correct answer: A. ((-3,5])

The first part is open up to (2), and the second starts at (2) included, so no gap remains. In exams, merge connected intervals.

Correct answer: C. (4)

Both intervals exclude (4), so (4) is not included. In exams, watch for missing open points even in a union.

Correct answer: B. (x\ge -1)

(-1) is included and the line goes right, so (x\ge -1). In exams, read ([ ) as including equality.

Correct answer: A. (x>7), so open circle at (7) and right side

Multiplying both sides by (3) gives (x-1>6), so (x>7). In exams, find the boundary first and then choose circle and direction.

Correct answer: C. Closed dot at (-2) and ray to the right

The sign (\ge) includes equality so the dot is closed. In exams always check the direction toward greater values.

Correct answer: B. Open dot at (-4) and closed dot at (1)

A round bracket endpoint is not included and a square bracket endpoint is included. In exams remember (() means open and ([) means closed.

Correct answer: D. (x<3.5)

The open dot shows that (3.5) is not included and the left direction shows smaller values. In exams write a strict inequality for an open dot.

Correct answer: A. Closed dot at (5) and ray to the right

Solving gives (x\ge 5) so (5) is included and the ray goes right. In exams simplify the inequality first then draw the number line.

Correct answer: C. ((0,6))

Open endpoints mean both (0) and (6) are not included. In exams write ((0,6)) for two open dots.

Correct answer: C. Open dot at (-6) and ray to the right

The sign (>) does not include equality so the dot is open. In exams draw the ray to the right for greater values.

Correct answer: B. (x\le -1)

The closed dot includes (-1) and the left direction shows smaller values. In exams use (\le) or (\ge) with a closed dot.

Correct answer: A. Open dot at (3) and ray to the left

Solving gives (x<3) so (3) is not included. In exams first find the boundary value then decide open or closed dot.

Correct answer: C. ((0,4))

Both open dots show that (0) and (4) are not included. In exams use round brackets for two open endpoints.

Correct answer: B. (x\ge 8)

The closed dot includes (8) and the right direction shows greater values. In exams choose (>) or (\ge) for a right ray.

Correct answer: A. ([-5,2))

The value (-5) is included and (2) is excluded so ([-5,2)) is correct. In exams use a square bracket at the equality endpoint.

Correct answer: D. Closed dot at (\frac{3}{2}) and ray left

The sign (\le) includes equality and smaller values lie to the left. In exams place a fractional boundary like any ordinary number.

Correct answer: C. (-3<x\le 6)

The open dot excludes (-3) and the closed dot includes (6). In exams write the shaded region as a compound inequality.

Correct answer: B. (x\le 2)

Solving gives (-2x\ge -4) and dividing by a negative changes the sign to (x\le 2). In exams reverse the inequality sign when dividing by a negative.

Correct answer: A. Closed dot at (9) and ray to the left

The interval ((-\infty,9]) includes (9) and all smaller values. In exams the ray toward (-\infty) goes left.

Correct answer: B. Open dot at (4) and the rest of the whole line

The inequality (x\ne 4) includes all real numbers except (4). In exams show the removed point as an open dot.

Correct answer: C. (-7) is excluded and (-2) is included

The round bracket excludes (-7) and the square bracket includes (-2). In exams the endpoint rule stays the same for negative numbers.

Correct answer: C. ((1,\infty))

The open dot excludes (1) and the right direction shows greater values. In exams infinity endpoints always use round brackets.

Correct answer: C. Closed dots at both (-1) and (3)

The interval ([-1,3]) has square brackets at both ends so both values are included. In exams draw closed dots for both endpoints of a closed interval.

Correct answer: B. (-8\le x\le 2)

Both closed dots show that (-8) and (2) are included. In exams connect closed dots with (\le) signs on both sides.

Correct answer: A. Closed dot at (-\frac{5}{2}) and ray right

Because of (\ge) the boundary value is included and greater values are to the right. In exams place the negative fraction correctly on the number line.