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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 {N, Z, or R} in each case. (a) x ≥ −2, where x ∈ Z. (b... 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 ≥ −2, where x ∈ Z.
Answer
For this inequality, x can take any integer value greater than or equal to -2. This includes values such as -2, -1, 0, 1, 2, 3, and so on. On the number line, we place a closed dot at -2 to indicate that this value is included. We then shade the line to the right to represent all integers greater than -2:
-4 -3 -2 ● -1 0 1 2 3 4
←→
Step 2
b) x ≥ −2, where x ∈ N.
Answer
In this case, x can take any natural number (positive integers) that is greater than or equal to -2. Since the smallest natural number is 0, the relevant values are 0, 1, 2, and so forth. A closed dot at -2 indicates inclusion, but focusing on N, we begin the line at 0. We represent this on the number line:
-4 -3 -2 ● 0 ● 1 2 3 4
←→
Step 3
c) x ≥ −2, where x ∈ R.
Answer
For real numbers, x includes all values greater than or equal to -2. This means we take all real values, including fractions and decimals. We place a closed dot at -2 to show it is included. The line is shaded to the right, indicating all numbers greater than -2:
-4 -3 -2 ● -1 0 1 2 3 4
←→