Z is the set of integers - Junior Cycle Mathematics - Question 12 - 2014
Question 12
Z is the set of integers. Explain what an integer is.
(i) Solve the inequality $-7+2x \leq 1$, where $x \in \mathbb{Z}$.
(ii) Graph your solution to (b)(i) on the ... show full transcript
Worked Solution & Example Answer:Z is the set of integers - Junior Cycle Mathematics - Question 12 - 2014
Step 1
Explain what an integer is.
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Answer
Integers are the set of all whole numbers. They include positive numbers, negative numbers, and zero. Formally, an integer is an element of the set {…,-3, -2, -1, 0, 1, 2, 3,…}.
Step 2
Solve the inequality $-7 + 2x \leq 1$.
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Answer
To solve the inequality, we first isolate the term containing x:
Add 7 to both sides:
2x≤1+72x≤8
Now divide both sides by 2:
x≤4
Therefore, the solution to the inequality is x≤4.
Step 3
Graph your solution to (b)(i) on the number line.
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Answer
To graph the solution x≤4:
We include the point at x=4 on the number line, as it is part of the solution (solid dot).
Shade to the left of 4 to indicate that all values less than 4 are included in the solution.
The final graph shows a solid dot at 4 and a line extending left towards negative infinity.
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