Question

solve the inequality. graph the solution.
-8 ≤ (2/5)(k - 2)
the solution is
blue square with white dot, various line and dot symbols, number line from -27 to 9 with ticks at -27, -24, -21, -18, -15, -12, -9, -6, -3, 0, 3, 6, 9 and arrows at both ends

Explanation:

Step1: Multiply both sides by 5/2

To eliminate the fraction, multiply both sides of the inequality \(-8 \leq \frac{2}{5}(k - 2)\) by \(\frac{5}{2}\).

$$ -8\times\frac{5}{2} \leq \frac{2}{5}(k - 2)\times\frac{5}{2} $$

Simplify the left side: \(-8\times\frac{5}{2}=-20\), and the right side simplifies to \(k - 2\). So we get \(-20 \leq k - 2\).

Step2: Add 2 to both sides

To solve for \(k\), add 2 to both sides of the inequality \(-20 \leq k - 2\).

$$ -20 + 2 \leq k - 2 + 2 $$

Simplify both sides: \(-18 \leq k\), which can also be written as \(k \geq -18\).

Answer:

\(k \geq -18\) (For the graph, we would use a closed dot at \(-18\) and an arrow pointing to the right, so we select the graph with a closed dot at \(-18\) and the arrow going to the right, which is the third graph from the top with the two open circles? Wait, no, re - evaluating the graph options: after solving \(k\geq - 18\), we need a closed dot at \(-18\) (since the inequality is "greater than or equal to") and the arrow should point to the right (towards positive infinity). Looking at the number line, \(-18\) is one of the marks. So the correct graph would have a closed dot at \(-18\) and an arrow going to the right. Among the given graph options, we need to identify the one with a closed dot at \(-18\) and the arrow to the right. If we assume the vertical options are for the dot type and direction, the one with a closed dot (filled circle) and the arrow pointing up (which represents going to the right on the number line? Wait, maybe the vertical arrows are indicating the direction on the number line. Wait, the number line has marks at \(-27, - 24, - 21, - 18, - 15, - 12, - 9, - 6, - 3, 0, 3, 6, 9\). So \(-18\) is a mark. So the solution \(k\geq - 18\) means we put a closed dot at \(-18\) and draw an arrow to the right (towards positive numbers). So in the given options, the graph with a closed dot at \(-18\) (the position corresponding to \(-18\) on the number line) and the arrow pointing to the right (maybe the one with the filled circle and the upward arrow, as upward on the vertical option would correspond to right on the horizontal number line) should be selected. But for the inequality solution, the algebraic solution is \(k\geq - 18\).

Final algebraic answer: \(\boldsymbol{k \geq -18}\)