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How many integral values of x satisfy |x + 1| + |x| + |x - 1| + | x - 2| = 7?
- a)0
- b)2
- c)1
- d)3
- e)Infinite
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
How many integral values of x satisfy |x + 1| + |x| + |x - 1| + | x - ...
Note th a t (x - 2), (x - 1), x and (x + 1) are four con secutive integers.
The magnitude of no set of four consecutive integers adds up to 7.
Hence, no integral values of x satisfy the given equation.
Hence, option 1.
The magnitude of no set of four consecutive integers adds up to 7.
Hence, no integral values of x satisfy the given equation.
Hence, option 1.
Most Upvoted Answer
How many integral values of x satisfy |x + 1| + |x| + |x - 1| + | x - ...
Given:
The equation to solve is: |x - 1| + |x| + |x - 1| + |x - 2| = 7.
Approach:
We will solve the equation by considering different cases based on the values of x.
Solution:
Case 1: x > 2
In this case, all the absolute values in the equation will be positive.
The equation becomes: (x - 1) + x + (x - 1) + (x - 2) = 7.
Simplifying the equation, we get: 4x - 5 = 7.
Solving for x, we get: x = 3.
Case 2: 1 < x="" ≤="" />
In this case, the absolute value of (x - 1) and (x - 2) will be positive, while the absolute value of x will be negative.
The equation becomes: (x - 1) - x + (x - 1) + (x - 2) = 7.
Simplifying the equation, we get: 2x - 3 = 7.
Solving for x, we get: x = 5.
Case 3: 0 < x="" ≤="" />
In this case, the absolute value of (x - 1) will be positive, while the absolute values of x and (x - 2) will be negative.
The equation becomes: (x - 1) - x - (x - 1) - (x - 2) = 7.
Simplifying the equation, we get: -2x + 2 = 7.
Solving for x, we get: x = -2.5, which is not an integral value.
Case 4: x ≤ 0
In this case, all the absolute values in the equation will be negative.
The equation becomes: -(x - 1) - x - (x - 1) - (x - 2) = 7.
Simplifying the equation, we get: -4x + 4 = 7.
Solving for x, we get: x = -0.75, which is not an integral value.
Therefore, the only integral values of x that satisfy the equation are x = 3 and x = 5.
Hence, the correct answer is option A) 0.
The equation to solve is: |x - 1| + |x| + |x - 1| + |x - 2| = 7.
Approach:
We will solve the equation by considering different cases based on the values of x.
Solution:
Case 1: x > 2
In this case, all the absolute values in the equation will be positive.
The equation becomes: (x - 1) + x + (x - 1) + (x - 2) = 7.
Simplifying the equation, we get: 4x - 5 = 7.
Solving for x, we get: x = 3.
Case 2: 1 < x="" ≤="" />
In this case, the absolute value of (x - 1) and (x - 2) will be positive, while the absolute value of x will be negative.
The equation becomes: (x - 1) - x + (x - 1) + (x - 2) = 7.
Simplifying the equation, we get: 2x - 3 = 7.
Solving for x, we get: x = 5.
Case 3: 0 < x="" ≤="" />
In this case, the absolute value of (x - 1) will be positive, while the absolute values of x and (x - 2) will be negative.
The equation becomes: (x - 1) - x - (x - 1) - (x - 2) = 7.
Simplifying the equation, we get: -2x + 2 = 7.
Solving for x, we get: x = -2.5, which is not an integral value.
Case 4: x ≤ 0
In this case, all the absolute values in the equation will be negative.
The equation becomes: -(x - 1) - x - (x - 1) - (x - 2) = 7.
Simplifying the equation, we get: -4x + 4 = 7.
Solving for x, we get: x = -0.75, which is not an integral value.
Therefore, the only integral values of x that satisfy the equation are x = 3 and x = 5.
Hence, the correct answer is option A) 0.
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