Which expressions would complete this equation so that it has infinitely many solutions?
\[ 8 + 2(8x - 6) = \]
Choose exactly two answers that are correct.
A. \(2(4x + 7)\)
B. \(9x - 10\)
C. \(16x - 4\)
D. \(4(4x - 1)\)
Answer (3)
8+2(8x-6)
=8+2(8x-6)
=8+16x-12
**=16x-4 **
=4(4x-1)
8 + 2 ( 8 x − 6 ) = 8 + 2 × 8 x + 2 × ( − 6 ) = 8 + 16 x − 12 = 16 x − 4 = 4 × 4 x − 4 × 1 = 4 ( 4 x − 1 ) A n s w er : D .
T h e e q u a t i o n ha s in f ini t e l y man y so l u t i o n s i f l e f t s i d e o f t hi s e q u a t i o n i s t ha t s am e l ik e r i g h t s i d e .
To have infinitely many solutions in the equation 8 + 2 ( 8 x − 6 ) = , the correct expressions are 16 x − 4 and 4 ( 4 x − 1 ) . These expressions equate to the simplified left side of the equation, ensuring an identity. Therefore, the choices are C and D.
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