Question

2/3x = 7 4/9 - 5 1/3

Answer 1

Ответ:2/3x=67/9-16*3/3

2/3x=19/9

19*3x=2*9

57x=18

x=18/57=6/19

Пошаговое объяснение:

Answer 2

To solve the equation 2/3x = 7 4/9 - 5 1/3, we need to simplify the right side first and then isolate the variable x.

Step 1: Simplify the right side To simplify 7 4/9 - 5 1/3, we first convert the mixed numbers to improper fractions.

7 4/9 = (7 * 9 + 4)/9 = 63/9 + 4/9 = 67/9 5 1/3 = (5 * 3 + 1)/3 = 16/3

Now, we can subtract these fractions: 67/9 - 16/3

To subtract fractions, we need to have a common denominator. The least common multiple of 9 and 3 is 9. We convert both fractions to have a denominator of 9.

67/9 - 16/3 = (67 * 3)/(9 * 3) - (16 * 3)/(3 * 3) = 201/27 - 48/9

Now, we have a common denominator of 27:

201/27 - 48/9 = 201/27 - (48 * 3)/(9 * 3) = 201/27 - 144/27

Now we can subtract the fractions:

201/27 - 144/27 = (201 - 144)/27 = 57/27 = 19/9

So, 7 4/9 - 5 1/3 simplifies to 19/9.

Step 2: Solve for x Now that we have simplified the equation to 2/3x = 19/9, we can solve for x.

To isolate x, we multiply both sides of the equation by the reciprocal of 2/3, which is 3/2:

(2/3x) * (3/2) = (19/9) * (3/2)

On the left side, the 3's cancel out, and on the right side, we can multiply the numerators and denominators:

x = (19 * 3)/(9 * 2) = 57/18

To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 3:

x = (57/3)/(18/3) = 19/6

Therefore, the solution to the equation 2/3x = 7 4/9 - 5 1/3 is x = 19/6.