Solve. | 8x - 3 | = x + 4  Enter your two answers separated by a comma. 

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baxthum8 | High School Teacher | (Level 3) Associate Educator

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Absolute value represents the distance from zero on a number line.  Therefore to solve this absolute value equation we must represent both distances from zero.  

Splittin this in to eqch equation makes the 2 equations given.

a)  `8x - 3 = x + 4`

       `7x = 7`

        `x = 1`

b)  `-(8x-3) = x + 4`

      `-8x + 3 = x + 4`

           `-9x = 1`

             `x = -1/9`

The solutions are `x = 1`  and `x = -1/9`

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tonys538 | Student, Undergraduate | (Level 1) Valedictorian

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The equation | 8x - 3 | = x + 4 has to be solved.

|8x - 3| = 8x - 3 for 8x - 3 >= 0 or x >= 3/8

and |8x - 3| = 3 - 8x for 8x - 3 <0 or x < 3/8.

If x >= 3/8, the given equation is 8x - 3 = x + 4 or 7x = 7 or x = 1

If x < 3/8, the given equation is 3 - 8x = x + 4 or -1 = 9x or x = -1/9

The solution of the equation | 8x - 3 | = x + 4 is x = 1 and x = -1/9

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