Questions: Solve and graph. -2 < 6-2x ≤ 8 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set in interval notation is B. There is no solution. Choose the graph of the solution set. A. C. D.

Solve and graph.
-2 < 6-2x ≤ 8

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The solution set in interval notation is
B. There is no solution.

Choose the graph of the solution set.
A.
C. D.

Transcript text: Solve and graph. \[ -2<6-2 x \leq 8 \] Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set in interval notation is $\square$ B. There is no solution. Choose the graph of the solution set. A. C. D.

Solution

Solution Steps

Step 1: Isolate the x term

Subtract 6 from all parts of the inequality:

-2 - 6 < -2x ≤ 8 - 6

-8 < -2x ≤ 2

Step 2: Divide by -2

Divide all parts of the inequality by -2. Remember to flip the inequality signs when dividing by a negative number.

-8 / -2 > x ≥ 2 / -2

4 > x ≥ -1

Step 3: Rewrite the inequality

Rewrite the inequality in standard form:

-1 ≤ x < 4

Step 4: Interval notation

The solution set in interval notation is [-1, 4).

Step 5: Choose the correct graph

The graph should show a closed circle at -1 and an open circle at 4, with the line shaded between them. This corresponds to option C.

Final Answer:

The solution set is [-1, 4), and the correct graph is C.

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