Question

symbols of inequalities diagnostic assessment

1. which letter identifies -1?

number line with points a, b, 0, c, d

1. what is the value identified by the dot on the number line?

number line with -3, -2, -1, 0, 1, 2, 3 and a dot

1. which letter or letters correctly represent x in the expression |x| = 2?

number line with points a(-2), b(-1), c(0), d(1), e(2)

1. complete the statement.

absolute value is the distance...

1. absolute value is always (choose one) positive/negative because...

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Explanation:

Question 1

Step1: Analyze the number line

The number line has points A, B, 0, C, D. The distance between 0 and B: since -1 is to the left of 0, let's see the intervals. From 0, moving left: B is one unit left (since each tick is 1 unit, assuming equal spacing). So -1 is at B.

Step1: Analyze the number line

The number line has -3, -2, -1, a dot, 0, 1, 2. The dot is halfway between -1 and 0? Wait, no, the ticks: from -1 to 0, how many intervals? Let's see, between -2 and -1: two small ticks? Wait, no, the number line: -3, then a tick, -2, then two ticks, -1, then a dot, then 0. Wait, the distance between -1 and 0: divided into two parts? Wait, the dot is at -0.5? Wait, no, let's check the spacing. From -3 to -2: one big tick, then a small tick? Wait, no, the given number line: -3, then a small tick, -2, then two small ticks, -1, then a dot, then 0. Wait, the dot is at -0.5? Wait, no, maybe the intervals: from -1 to 0, the dot is at -0.5? Wait, no, let's count the units. From -1 to 0: the dot is halfway? Wait, the number line: -3, -2, -1, (dot), 0. The dot is at -0.5? Wait, no, maybe the spacing is 0.5? Wait, between -1 and 0, there are two small ticks? Wait, the number line shows: -3, then a tick, -2, then two ticks, -1, then a dot, then 0. So from -1 to 0, the dot is at -0.5? Wait, no, maybe the dot is at -0.5? Wait, no, let's see: the distance between -1 and 0 is 1 unit, divided into two equal parts (since there's one dot in between). So each part is 0.5. So the dot is at -1 + 0.5 = -0.5? Wait, no, from -1 moving towards 0, the first tick (dot) is at -0.5? Wait, yes. So the value is -0.5.

Step1: Recall absolute value definition

The equation \(|x| = 2\) means \(x = 2\) or \(x = -2\) (since absolute value is distance from 0, so numbers 2 units from 0 are 2 and -2).

Step2: Identify on the number line

On the number line, A is at -2, E is at 2. So A and E represent x such that \(|x| = 2\).

Answer:

B

Question 2