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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 $x \in \mathbb{N}$.
Answer
To graph the inequality for natural numbers ( ( \mathbb{N} )), we start by identifying the relevant natural numbers that satisfy this inequality. The natural numbers less than 4 are 0, 1, 2, and 3.
On the number line, we represent these points with solid dots at 0, 1, 2, and 3, and an open circle at 4 to indicate that 4 is not included in the solution. The line extends to the left, indicating all values less than 4 are acceptable.
Step 2
(ii) $x < 4$, where $x \in \mathbb{Z}$.
Answer
For integers ( ( \mathbb{Z} )), we identify the integers that satisfy the inequality . These integers include ..., -3, -2, -1, 0, 1, 2, and 3.
On the number line, we denote the integers less than 4 with solid dots at -3, -2, -1, 0, 1, 2, and 3, and again, an open circle at 4 to show that this value is not included.
Step 3
(iii) $x < 4$, where $x \in \mathbb{R}$.
Answer
For real numbers ( ( \mathbb{R} )), the solution set for includes all values less than 4.
On the number line, we represent this inequality with an open circle at 4, indicating that 4 is not included, and a solid line extending to the left, illustrating that all values less than 4 are included in the solution.