Which expression below is equivalent to \(\frac{4}{3}x + \frac{14}{3}\)?

A. \(\frac{4}{3}(x + 2)\)

B. \(\frac{1}{3}(4x + 6)\)

C. \(\frac{2}{3}(2x + 4)\)

D. \(\frac{2}{3}(2x + 7)\)

I assume that 4 2/3 is 4 and 2/3, not 4 * 2/3. If so, 4 2/3 is as much as 14/3.
A. 4/3 (x + 2) = 4/3x + 8/3 B. 1/3 (4x + 6) = 4/3x + 2 C. 2/3 (2x + 4) = 4/3x + 8/3 D. 2/3 (2x + 7) = 4/3x + 14/3
It means that D is correct.

Answered by SlowZasob | 2024-06-10

** An equivalent expression is:**
3 2 ​ ( 2 x + 7 )
** Option D** ; For this case we have the following expression:
3 4 ​ x + 4 3 2 ​
The first thing we must do for this case is to write the mixed number as a fraction.
We have then:
3 4 ​ x + 3 14 ​
Then, we can do common factor 2/3 in the expression.
We have then:
3 2 ​ ( 2 x + 7 )

Answered by carlosego | 2024-06-11

The equivalent expression to 3 4 ​ x + 3 14 ​ is 3 2 ​ ( 2 x + 7 ) , which corresponds to option D. By factoring out 3 2 ​ from both terms, we arrive at this expression.
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Answered by carlosego | 2024-12-23