The solution for the absolute value equation is x = 10 and x = -14
In this question,
Two thirds times the absolute value of the quantity x plus 2 end quantity minus 8 equals 0. The equation for this statement is 2/3 lx + 2l -8 =0.
The solution for the equation is
[tex]\frac{2}{3}[/tex] lx + 2l -8 =0
[tex]\frac{2}{3}[/tex] lx + 2l = 8
Multiply by 3/2 on both sides,
[tex]\frac{2}{3}[/tex] lx + 2l = 8
[tex]\frac{2}{3}[/tex] ×[tex]\frac{3}{2}[/tex]lx + 2l =8×[tex]\frac{3}{2}[/tex]
=> x +2 = 12
Case 1: Take as positive value
=> x + 2 = 12
=> x = 12 - 2
=> x = 10
Case 2: Take as negative value
=> -(x +2) = 12
=> -x - 2 = 12
=> -x = 12 + 2
=> -x = 14
=> x = -14
Hence, we can conclude that the solution for the absolute value equation is x = 10 and x = -14 is the correct answer
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