To calculate: The solution of absolute value equation and write solution set in interval notation. a) |x−1|=|3x+5| b) |x−1|=|x+5| c) |x−1|=|1−x|

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To calculate:  The solution of absolute value equation and write solution set in interval notation.  a) |x−1|=|3x+5|   b) |x−1|=|x+5|  c) |x−1|=|1−x|

Lupe Kirkland · Accepted Answer

Step 1  Consider the provided equation |x−1|=|3x+5|  The equation is in the form |u|=|k|, where u=x−1  Thus, the equation |x−1|=|3x+5| is equivalent to  x−1=3x+5 or x−1=−(3x+5)  −1−5=3x−x or 4x=−4  −6=2x or 4x=−4  x=−3 or x=−1  Therefore, the solution set is {x∣−3≤x≤−1} and the solution in interval notation is {−3, −1}

mylouscrapza · Accepted Answer

Step 1  Consider the provided equation |x−1|=|x+5|  The equation is in the form |u|=|k|, where u=x−1  Thus, the equation |x−1|=|x+5| is equivalent to  x−1=x+5 or x−1=−(x+5)  −1−5=x−x or x+x=−5+1  −6=0 or 2x=−4  −6=0 or x=−2  Since, −6=0 is not possible, therefore, x=−2 is valid.  Therefore, the solution set is {x∣x=−2} and the solution in interval notation is {−2}

user_27qwe · Accepted Answer

Step 1 Consider the provided equation |x−1|=|1−x| The equation is in the form |u|=|k|, where u=x−1 Thus, the equation |x−1|=|1−x| is equivalent to x−1=1−x or x−1=−(1−x) x+x=1+1 or x−x=−1+1 2x=2 or 0=0 x=1 or 0=0 Therefore, the solution set is R and the solution in interval notation is −∞, ∞

To calculate: The solution of absolute value equation and write solution set

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