Math, asked by mehul517, 3 months ago

Sum of values x satisfying the equation
|x+1|=|2x-4|

Answers

Answered by karthikag10a
1

Step-by-step explanation:

x + 1 = 2x - 4

Bringing 2x to LHS & 1 to RHS :

x - 2x = -4 -1

- x = - 5

x = 5

Answered by itzbangtanarmy7
2

Answer:

For a,b∈Ra,b∈R , think of |a−b||a−b| as the distance between aa and bb on the real line. Thus, we seek all xx on the real line for which the sum of distances between xx and aa and between xx and bb equals 11 .

If xx lies between 22 and 33 , then this sum equals the distance between 22 and 33 , and hence equals 11 . This applies to the end points x=2x=2 and x=3x=3 as well. Thus, this equality holds for x∈[2,3]x∈[2,3] .

On the other hand, if xx lies to the right of 33 or to the left of 22 , its distance from the opposite end exceeds 11 . Hence, the sum of distances can’t equal 11 .

Therefore, {x∈R:|x−2|+|x−3|=1}={x∈R:2≤x≤3}{x∈R:|x−2|+|x−3|=1}={x∈R:2≤x≤3}

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