Representing integers on the number line

Draw a number line in your notebook and represent the following integers on it:

You can do it on paper and send a photo with your answer.

Represent the number $-3$ and its opposite on the number line. How far is each one from the origin?

You can use this number line, in which the origin and the units are marked (each mark is one unit), or draw your own:

You can do it on paper and send a photo with your answer.

In a ski resort in Sierra Nevada, the thermometer recorded the following temperatures throughout the morning:

• At 8:00: $-6$ $^\circ$C

• At 10:00: $-2$ $^\circ$C

• At 12:00: $+3$ $^\circ$C

1. a) Represent the three temperatures on a vertical number line (like a thermometer).
2. b) What was the temperature change (distance on the line) between 8:00 and 12:00?

Find the integer that is exactly the same distance from $-7$ and from $+3$ on the number line. In the figure those two numbers are marked. Represent it graphically on the line to check your result and explain how you calculated it.

Write in your notebook all the integers $x$ that satisfy the condition $-2 < x \leq 3$ and represent them on the number line. Pay close attention to the open and closed endpoints.

You can copy this number line into your notebook:

Write down all the integers $x$ that satisfy the following two conditions simultaneously and represent them on a number line:

• $-5 < x \leq 2$

• The absolute value of $x$ is greater than $1$, that is, $|x| > 1$.

Represent on the number line all the integers whose absolute value is equal to $4$. How many numbers have you marked?

You can do it on paper and send a photo with your answer.

Given the following expressions, place on the number line the values of $x$ that make them true:

1. a) $|x - 3| = 5$
2. b) $|x - 2| = 4$

Which integer is a solution to both expressions at the same time? Mark it with a different colour on your line.