|2/3 x – 4| = 10
A. Ø
B. {-21,21}
C. {-9,21}
D. {-4, 9 1/3}
E. {-21, 9}
|2/3 x – 4| = 10
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|2/3 x – 4| = 10
A. Ø
B. {-21,21}
C. {-9,21}
D. {-4, 9 1/3}
E. {-21, 9}
To solve the equation (|frac{2}{3}x – 4| = 10), we need to consider the two cases that arise from the absolute value.
1. Case 1: (frac{2}{3}x – 4 = 10)
Adding 4 to both sides:
(frac{2}{3}x = 14)
Now, multiply both sides by (frac{3}{2}):
(x = 21)
2. Case 2: (frac{2}{3}x – 4 = -10)
Adding 4 to both sides:
(frac{2}{3}x = -6)
Now, multiply both sides by (frac{3}{2}):
(x = -9)
Putting both solutions together, we find (x = -9) and (x = 21).
The correct answer is C. {-9, 21}.