What are the solutions to the equation | 2/3 x – 4 | = 10?

Question

| 2/3 x – 4 | = 10 A. Ø B. {-21, 21} C. {-9, 21} D. {-4, 9 1/3} E. {-21, 9}

Quizzma Team · Answer

To solve the equation |2/3 x – 4| = 10, we need to consider both scenarios for the absolute value.

1. First case:

( 2/3 x – 4 = 10 )

– Add 4 to both sides:

( 2/3 x = 14 )

– Multiply by ( 3/2 ):

( x = 21 )

2. Second case:

( 2/3 x – 4 = -10 )

– Add 4 to both sides:

( 2/3 x = -6 )

– Multiply by ( 3/2 ):

( x = -9 )

Therefore, the solutions are ( x = 21 ) and ( x = -9 ).

The correct answer is C. {-9, 21}.

1 Answer