MATHEMATICS
JAMB 2013 - Question 18
Mathematics 2013 JAMB Past Questions - Question 18: Solve for x:|x-2|< 3
A:
B:
C:
D:
Correct Answer
D
Explanation
< 3implies-(x-2) < 3 or + (x-2) <3-x+2<3- x< 3 - 2- x < 1- x /- 1 > 1/-1x >-1 OR -1 combining the two inequalities results, we get -1To solve the inequality |x - 2| < 3, we need to consider two cases: when the expression inside the absolute value is positive and when it is negative.Case 1: x - 2 > 0In this case, the absolute value expression simplifies to x - 2 < 3. Solving for x, we have:x < 3 + 2x < 5Case 2: x - 2 < 0In this case, the absolute value expression simplifies to -(x - 2) < 3. Multiplying both sides by -1, we have:x - 2 > -3x > -3 + 2x > -1Combining the solutions from both cases, we have:-1 < x < 5Therefore, the solution to the inequality |x - 2| < 3 is -1 < x < 5.
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