Graph each of the following inequalities on the number line given - Junior Cycle Mathematics - Question b - 2016
Question b
Graph each of the following inequalities on the number line given.
(i) $x < 4$, where $x \in \mathbb{N}$.
(ii) $x < 4$, where $x \in \mathbb{Z}$.
(iii) $x < 4$, w... show full transcript
Worked Solution & Example Answer:Graph each of the following inequalities on the number line given - Junior Cycle Mathematics - Question b - 2016
Step 1
(i) $x < 4$, where $x \in \mathbb{N}$.
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Answer
To graph the inequality x<4 for natural numbers, the natural numbers are 1, 2, 3. Therefore, on the number line:
Draw an open circle at 4 to indicate that 4 is not included.
Shade the numbers 1, 2, and 3 to show that these values satisfy the inequality.
Step 2
(ii) $x < 4$, where $x \in \mathbb{Z}$.
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Answer
For this part, we consider integers. The integers satisfying the inequality x<4 are ... -3, -2, -1, 0, 1, 2, 3. In the graph:
Again, draw an open circle at 4.
Shade from -3 to 3, including -3, -2, -1, 0, 1, 2, and 3.
Step 3
(iii) $x < 4$, where $x \in \mathbb{R}$.
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Answer
Here, we include all real numbers less than 4. Thus, the graph:
Has an open circle at 4.
Shades everything to the left of 4, indicating that all real numbers, including decimals, up to just before 4, satisfy the condition.
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