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Which of the following values are solutions to the inequality -10 <= 2x+10 ? I. -13 II. -2 III. -10 None I only II only III only I and II I and III II and III I, II and III

Which of the following values are solutions to the inequality −10≤2x+10 -10 \leq 2 x+10 ?\newlineI. −13-13\newlineII. −2-2\newlineIII. −10-10\newlineNone\newlineI only\newlineII only\newlineIII only\newlineI and II\newlineI and III\newlineII and III\newlineI, II and III

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Q. Which of the following values are solutions to the inequality −10≤2x+10 -10 \leq 2 x+10 ?\newlineI. −13-13\newlineII. −2-2\newlineIII. −10-10\newlineNone\newlineI only\newlineII only\newlineIII only\newlineI and II\newlineI and III\newlineII and III\newlineI, II and III
  1. Understand and Isolate x: Understand the inequality and isolate x. The inequality given is −10≤2x+10-10 \leq 2x + 10. To find the solutions for x, we need to isolate x on one side of the inequality. Subtract 1010 from both sides of the inequality to isolate the term with x. −10−10≤2x+10−10-10 - 10 \leq 2x + 10 - 10 −20≤2x-20 \leq 2x Now, divide both sides by 22 to solve for x. −20/2≤2x/2-20 / 2 \leq 2x / 2 −10≤x-10 \leq x This means that any value of x that is greater than or equal to −10-10 is a solution to the inequality.
  2. Test −13-13: Test the first value, I. −13-13. We need to check if x=−13x = -13 is a solution to the inequality −10≤x-10 \leq x. −13-13 is not greater than or equal to −10-10. Therefore, −13-13 is not a solution to the inequality.
  3. Test −2-2: Test the second value, II. −2-2.\newlineWe need to check if x=−2x = -2 is a solution to the inequality −10≤x-10 \leq x.\newline−2-2 is greater than −10-10.\newlineTherefore, −2-2 is a solution to the inequality.
  4. Test −10 -10 : Test the third value, III. −10 -10 .\newlineWe need to check if x=−10 x = -10 is a solution to the inequality −10≤x -10 \leq x .\newline−10 -10 is equal to −10 -10 .\newlineTherefore, −10 -10 is a solution to the inequality.
  5. Combine Results: Combine the results from Steps 22, 33, and 44 to find the correct answer.\newlineFrom Step 22, we found that −13-13 is not a solution.\newlineFrom Step 33, we found that −2-2 is a solution.\newlineFrom Step 44, we found that −10-10 is a solution.\newlineThe correct answer is that the values −2-2 and −10-10 are solutions to the inequality.

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