Which of the following values are solutions to the inequality 8-4 x>-9 ? I. −2II. 7III. 12NoneI onlyII onlyIII onlyI and III and IIIII and IIII, II and III
Q. Which of the following values are solutions to the inequality 8−4x>−9?I. −2II. 7III. 12NoneI onlyII onlyIII onlyI and III and IIIII and IIII, II and III
Understand Inequality: Understand the inequality and what it means to be a solution.To be a solution to the inequality 8-4x > -9, a value for x must make the inequality true when substituted into the inequality.
Test Value −2: Test the first value, I.−2. Substitute x=−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 16 is greater than −9, the inequality is true.
Test Value 7: Test the second value, II. 7.Substitute x=7 into the inequality.8 - 4(7) > -9Calculate the left side of the inequality.8 - 28 > -9-20 > -9Check if the inequality holds true.Since −20 is not greater than −9, the inequality is false.
Test Value 12: Test the third value, III. 12. Substitute x=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 is not greater than −9, the inequality is false.
Combine Results: Combine the results from the previous steps to determine which values are solutions.From Step 2, we found that x=−2 is a solution.From Step 3 and Step 4, we found that x=7 and x=12 are not solutions.Therefore, the only value that is a solution to the inequality is −2.