Question

solve the inequality and graph the solution set. write the answer in interval notation. write your answer in exact simplified form.
-0.2 < 3 + 8k < 7
part 1 of 2
the solution is ( -0.4, 0.5 ).
{ } (□,□) □,□
(□,□ □,□) □∪□
∞ -∞ □/□
part 2 of 2
number line from -2 to 3 with tick marks ( )

Explanation:

Step1: Subtract 3 from all parts

To isolate the term with \( k \), we subtract 3 from each part of the compound inequality.
\( -0.2 - 3 < 3 + 8k - 3 < 7 - 3 \)
\( -3.2 < 8k < 4 \)

Step2: Divide all parts by 8

To solve for \( k \), we divide each part of the inequality by 8.
\( \frac{-3.2}{8} < \frac{8k}{8} < \frac{4}{8} \)
\( -0.4 < k < 0.5 \)

In interval notation, this is \( (-0.4, 0.5) \).

For the graph: We use open circles at \( -0.4 \) and \( 0.5 \) (since the inequality is strict, \( < \) not \( \leq \)) and draw a line segment between them on the number line.

Answer:

Part 1: The solution in interval notation is \(\boldsymbol{(-0.4, 0.5)}\).

Part 2: On the number line, place open circles at \(-0.4\) and \(0.5\) and draw a line connecting them between these two points.