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Graph each of the following inequalities on the number line given - Junior Cycle Mathematics - Question 10 - 2016
Question 10
Graph each of the following inequalities on the number line given. Note: $x$ is an element of a different set $( ext{N, Z, or R})$ in each case. (a) $x < 4$, where ... show full transcript
Worked Solution & Example Answer:Graph each of the following inequalities on the number line given - Junior Cycle Mathematics - Question 10 - 2016
Step 1
(a) $x < 4$, where $x \\in \mathbb{N}$
Answer
To graph the inequality where is a natural number, we represent the natural numbers less than 4: 1, 2, 3.
On the number line, these are indicated by solid circles at 1, 2, and 3, since they are included, and an open circle at 4, indicating that 4 is not included. The graph would appear as follows:
-5 -4 -3 -2 -1 0 1 2 3 4 5
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Step 2
(b) $x < 4$, where $x \\in \mathbb{Z}$
Answer
In this case, is an integer less than 4. Thus, the integers satisfying this inequality are: -5, -4, -3, -2, -1, 0, 1, 2, and 3.
The number line representation will have solid circles at all these integer points up to 3, and an open circle at 4, showing that 4 is excluded:
-5 -4 -3 -2 -1 0 1 2 3 4 5
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Step 3
(c) $x < 4$, where $x \\in \mathbb{R}$
Answer
For this part, can be any real number less than 4. The graph will show a continuous line all the way up to but not including 4.
The number line is depicted with an open circle at 4 to signify it is not included:
-5 -4 -3 -2 -1 0 1 2 3 4 5
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