Which of the following values are solutions to the inequality 2 x+2>-9 ? I. −14II. −11III. −7NoneI onlyII onlyIII onlyI and III and IIIII and IIII, II and III
Q. Which of the following values are solutions to the inequality 2x+2>−9?I. −14II. −11III. −7NoneI onlyII onlyIII onlyI and III and IIIII and IIII, II and III
Isolate variable x: Isolate the variable x in the inequality 2x + 2 > -9 by subtracting 2 from both sides of the inequality.Calculation: 2x + 2 - 2 > -9 - 2Simplified: 2x > -11
Divide by 2: Divide both sides of the inequality 2x > -11 by 2 to solve for x.Calculation: \frac{2x}{2} > \frac{-11}{2}Simplified: x > -5.5
Check −14: Check if the value I, which is −14, is a solution to the inequality x > -5.5.Calculation: -14 > -5.5This is not true, so −14 is not a solution.
Check −11: Check if the value II, which is −11, is a solution to the inequality x > -5.5.Calculation: -11 > -5.5This is not true, so −11 is not a solution.
Check −7: Check if the value III, which is −7, is a solution to the inequality x > -5.5.Calculation: -7 > -5.5This is true, so −7 is a solution.
Identify solutions: Based on the checks in steps 3, 4, and 5, only the value III (−7) is a solution to the inequality.
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