Question

apply it
1 write two inequalities that compare the value of point p and the value of
point q. show your work.
(number line with p near -1 and q near 0)
solution

Explanation:

Step1: Identify values of P and Q

On the number line, P is at $-\frac{4}{5}$ (since it's 4/5 left of 0, between -1 and 0, 1 unit divided into 5 parts? Wait, no, looking at the number line: from -1 to 0, how many ticks? Wait, P is at -0.8? Wait, no, let's count the ticks. From -1 to 0: P is at the first tick after -1? Wait, no, the number line: -1, then P, then some ticks, then 0, then Q. Wait, actually, let's see: Q is at $\frac{1}{5}$ (since from 0 to 1, divided into 5 parts? Wait, no, the distance from 0 to 1 has 5 ticks? Wait, no, the number line: from -1 to 0, how many intervals? Let's see, P is at -0.8 (since -1 to 0 is 1 unit, divided into 5 parts? Wait, no, maybe each tick is 0.2? Wait, -1, then P at -0.8, then -0.6, -0.4, -0.2, 0, then Q at 0.2. Wait, yes, because from -1 to 0: 5 intervals (since between -1 and 0, there are 5 ticks? Wait, the number line shows: -1, then P (a dot), then 4 more ticks to 0, then Q (a dot) at the first tick after 0, then 4 more ticks to 1. So each interval is 0.2 (since 1 unit / 5 intervals = 0.2 per interval). So P is at -0.8 (which is $-\frac{4}{5}$) and Q is at 0.2 (which is $\frac{1}{5}$).

Step2: Write first inequality (P < Q)

Since P is negative and Q is positive, $-\frac{4}{5} < \frac{1}{5}$ (or -0.8 < 0.2).

Step3: Write second inequality (Q > P)

Which is the reverse of the first, so $\frac{1}{5} > -\frac{4}{5}$ (or 0.2 > -0.8).

Answer:

Two inequalities are $P < Q$ (e.g., $-\frac{4}{5} < \frac{1}{5}$) and $Q > P$ (e.g., $\frac{1}{5} > -\frac{4}{5}$) (or using decimals: $-0.8 < 0.2$ and $0.2 > -0.8$).