Solve the compound inequality. Express the solution using interval notation. Graph the solution set.
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Question

Quizplus · Accepted Answer

The compound inequality is -6 ≤ 3x - 5 < 3. To solve it, we add 5 to all the terms: -1 ≤ 3x < 8, and then divide by 3: -1/3 ≤ x < 8/3. This solution is expressed in interval notation as [-1/3, 8/3). To graph it, we draw a closed circle at -1/3 (since it's included in the solution set) and an open circle at 8/3 (since it's not included), and shade the interval between them. The graph matches choice B. The compound inequality is:

-4x - 6 ≥ 18 or -4x - 6 < -22

Solving each inequality separately:

-4x - 6 ≥ 18

-4x ≥ 24

x ≤ -6

and

-4x - 6 < -22

-4x < -16

x > 4

Putting these together in interval notation, we have:

(-∞, -6] ∪ (4, ∞)

Graphing this on a number line would give an open circle at -6 and another open circle at 4, with shaded regions to the left of -6 and to the right of 4. The union of these shaded regions represents the solution set.

Solve the Compound Inequality