The solution for the absolute value equation is option (A) x = -15 and x = 21 is the correct answer.
In this question,
One third times the absolute value of the quantity x minus 3 end quantity plus 4 equals 10. The equation for this statement is 1/3 |x - 3| + 4 = 10.
The solution for the equation is
[tex]\frac{1}{3}[/tex] |x - 3| + 4 = 10
⇒ [tex]\frac{1}{3}[/tex] |x - 3| = 10 - 4
⇒ [tex]\frac{1}{3}[/tex] |x - 3| = 6
Multiply by 3 on both sides,
⇒ [tex]\frac{1}{3}[/tex] |x - 3| = 6
⇒ [tex]\frac{3}{3}[/tex] |x - 3| = 18
The absolute value of the equation takes both as positive and negative values.
Case 1: Take as positive value
⇒ x - 3 = 18
⇒ x = 18 + 3
⇒ x = 21
Case 2: Take as negative value
⇒ - (x-3) = 18
⇒ -x + 3 = 18
⇒ x = 3 - 18
⇒ x = -15
Hence we can conclude that the solution for the absolute value equation is option (A) x = -15 and x = 21 is the correct answer.
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