Questions: HW Unit 1 - Linear Inequalities Question 34 of 38 (1 point) Question Attempt: 2 of Unlimited Graph the solution set, and write the solution set in interval notation. -1 < a/6 ≤ 1

HW Unit 1 - Linear Inequalities Question 34 of 38 (1 point) Question Attempt: 2 of Unlimited Graph the solution set, and write the solution set in interval notation. -1 < a/6 ≤ 1
Transcript text: HW Unit 1 - Linear Inequalities Question 34 of 38 (1 point) | Question Attempt: 2 of Unlimited Graph the solution set, and write the solution set in interval notation. \[ -1<\frac{a}{6} \leq 1 \] Part 1 of 2
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Solution

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Solution Steps

Step 1: Multiply by 6

To isolate \(a\), we multiply all parts of the compound inequality by 6. \[ -1 \cdot 6 < \frac{a}{6} \cdot 6 \leq 1 \cdot 6 \] \[ -6 < a \leq 6 \]

Step 2: Graph the solution set

On the number line, the solution set includes all numbers greater than -6 and less than or equal to 6. Since -6 is not included, we use an open circle at -6. Since 6 is included, we use a closed circle at 6. The solution set is all numbers between -6 and 6, including 6.

Step 3: Write the solution set in interval notation

The interval notation for this solution set is \((-6, 6]\). The parenthesis indicates that -6 is not included in the interval, and the bracket indicates that 6 is included.

Final Answer

The solution set is \(\boxed{(-6, 6]}\).

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