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Which of the following values are solutions to the inequality 
8-4x > -9?
I. -2
II. 7
III. 12
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 8-4 x>-9 ? \newlineI. 2-2\newlineII. 77\newlineIII. 1212\newlineNone\newlineI only\newlineII only\newlineIII only\newlineI and II\newlineI and III\newlineII and III\newlineI, II and III

Full solution

Q. Which of the following values are solutions to the inequality 84x>9? 8-4 x>-9 ? \newlineI. 2-2\newlineII. 77\newlineIII. 1212\newlineNone\newlineI only\newlineII only\newlineIII only\newlineI and II\newlineI and III\newlineII and III\newlineI, II and III
  1. Understand Inequality: Understand the inequality and what it means to be a solution.\newlineTo be a solution to the inequality 8-4x > -9, a value for xx must make the inequality true when substituted into the inequality.
  2. Test Value 2-2: Test the first value, I.2I. -2. Substitute x=2x = -2 into the inequality. 8 - 4(-2) > -9 Calculate the left side of the inequality. 8 + 8 > -9 16 > -9 Check if the inequality holds true. Since 1616 is greater than 9-9, the inequality is true.
  3. Test Value 77: Test the second value, II. 77.\newlineSubstitute x=7x = 7 into the inequality.\newline8 - 4(7) > -9\newlineCalculate the left side of the inequality.\newline8 - 28 > -9\newline-20 > -9\newlineCheck if the inequality holds true.\newlineSince 20-20 is not greater than 9-9, the inequality is false.
  4. Test Value 1212: Test the third value, III. 1212. Substitute x=12x = 12 into the inequality. 8 - 4(12) > -9 Calculate the left side of the inequality. 8 - 48 > -9 -40 > -9 Check if the inequality holds true. Since 40-40 is not greater than 9-9, the inequality is false.
  5. Combine Results: Combine the results from the previous steps to determine which values are solutions.\newlineFrom Step 22, we found that x=2x = -2 is a solution.\newlineFrom Step 33 and Step 44, we found that x=7x = 7 and x=12x = 12 are not solutions.\newlineTherefore, the only value that is a solution to the inequality is 2-2.

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