Question

Given the equation ( frac1/5 + frac2/3 |2-x| = frac4/15 ), which of the following is true?

a) ( frac2/3|2-x| = frac1/15 )
b) ( frac13/15|2-x| = frac4/15 )
c) ( |2-x| = frac1/10 )
d) ( frac1/5 + | frac4/3 - frac2/3x | = frac4/15 )

Answer 1

Upon simplifying the provided equation (1/5 + 2/3 |2-x| = 4/15), we find that the correct statement is option (c), which is |2-x| = 1/10.

The correct answer is C.

Step-by-step explanation:

To determine which of the option statements is true given the equation (1/5 + 2/3 |2-x| = 4/15), we need to simplify and solve the equation. We begin by finding a common denominator for the fractions 1/5 and 4/15 which is 15. Multiplying each term by 15 to eliminate the fractions gives us:

3 + 10|2-x| = 4

Now we subtract 3 from each side of the equation to isolate the term with the absolute value:

10|2-x| = 1

Dividing both sides by 10 gives us:

|2-x| = 1/10

This corresponds to option (c), which states that |2-x| = 1/10 is true. The other options cannot be correct because they either involve different numbers or operations that do not match the simplified form of our original equation.