solve for k and graph the solution. k - 8 ≥ 1 + 4k or -10k + 7 + 4k ≤ 19. plot the endpoints. select an…

solve for k and graph the solution. k - 8 ≥ 1 + 4k or -10k + 7 + 4k ≤ 19. plot the endpoints. select an endpoint to change it from closed to open. select the middle of a segment, ray, or line to delete it.

solve for k and graph the solution. k - 8 ≥ 1 + 4k or -10k + 7 + 4k ≤ 19. plot the endpoints. select an endpoint to change it from closed to open. select the middle of a segment, ray, or line to delete it.

Answer

Answer:

The solution of the compound - inequality is (k\leq2).

Explanation:

Step1: Solve the first inequality

Solve (k - 8\geq1 + 4k). Subtract (k) from both sides: (-8\geq1 + 3k). Subtract 1 from both sides: (-9\geq3k). Divide both sides by 3: (k\leq - 3).

Step2: Solve the second inequality

Solve (-10k+7 + 4k\leq19). Combine like - terms: (-6k+7\leq19). Subtract 7 from both sides: (-6k\leq12). Divide both sides by (-6) and reverse the inequality sign: (k\geq - 2).

Step3: Analyze the 'or' compound - inequality

The compound inequality is (k - 8\geq1 + 4k) or (-10k + 7+4k\leq19). The solutions of the two inequalities are (k\leq - 3) or (k\geq - 2). To graph:

  • For (k\leq - 3), we have a closed circle at (k=-3) (if the original inequality was non - strict) and an arrow pointing to the left.
  • For (k\geq - 2), we have a closed circle at (k = - 2) (if the original inequality was non - strict) and an arrow pointing to the right. If we consider the operations of changing endpoints and deleting lines as per the additional instructions in the problem (which seem a bit out of context for the pure solution of the inequality but for the full - scope problem): The overall solution set of the compound inequality in interval notation is ((-\infty,-3]\cup[-2,\infty)). When graphing on the number line provided, we mark the points (-3) and (-2) and draw the appropriate rays. If we had to perform the operations like changing an endpoint from closed to open or deleting a line, it would depend on further specific interpretations of those non - standard instructions. But the solution of the compound inequality itself is (k\leq - 3) or (k\geq - 2), which can be combined and simplified to (k\in R\setminus(-3,-2)) or in a more basic form considering the two separate inequalities results, we can say the combined result for the values of (k) that satisfy the compound inequality is (k\leq2) (by considering all real numbers that make either of the original inequalities true).