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What is the range of the solutions to the equation |2x − 3| = 7?
- a)4
- b)5
- c)6
- d)7
- e)8
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
What is the range of the solutions to the equation |2x − 3| = 7?...
We can split the equation into two cases, one for the positive value inside the absolute value and one for the negative value inside:
Case 1: 2x - 3 = 7
Solving this equation, we have:
2x - 3 = 7
Adding 3 to both sides:
2x = 10
Dividing both sides by 2:
x = 5
Solving this equation, we have:
2x - 3 = 7
Adding 3 to both sides:
2x = 10
Dividing both sides by 2:
x = 5
Case 2: -(2x - 3) = 7
Solving this equation, we have:
-(2x - 3) = 7
Multiplying both sides by -1 and distributing the negative sign:
-2x + 3 = 7
Subtracting 3 from both sides:
-2x = 4
Dividing both sides by -2 (which flips the inequality direction):
x = -2
Solving this equation, we have:
-(2x - 3) = 7
Multiplying both sides by -1 and distributing the negative sign:
-2x + 3 = 7
Subtracting 3 from both sides:
-2x = 4
Dividing both sides by -2 (which flips the inequality direction):
x = -2
Therefore, the solutions to the equation are x = 5 and x = -2.
The range of solutions refers to the difference between the largest and smallest values. In this case, it is the absolute difference between 5 and -2, which is 7. Thus, the range of solutions to the equation |2x - 3| = 7 is 7.
Therefore, the correct answer is D: 7.
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What is the range of the solutions to the equation |2x − 3| = 7?a)4b)5c)6d)7e)8Correct answer is option 'D'. Can you explain this answer?
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