Question

2 3/5+(x-2 1/6)=5 2/3​

Answer 1

Ответ:

$2 \frac{3}{5} + (x - 2 \frac{1}{6} ) = 5 \frac{2}{3} \\ 2 \frac{3}{5} + x - 2 \frac{1}{6} = 5 \frac{2}{3} \\ \frac{5*2+3}{5} + x - \frac{6*2+1}{6} = \frac{3*5+2}{3} \\ \frac{13}{5} + x - \frac{13}{6} = \frac{17}{3} \\ x = \frac{17}{3} - \frac{13}{5} + \frac{13}{6} \\x = \frac{170-78+65}{30} \\ x = \frac{157}{30} \\ x = 5 \frac{7}{30}$

Answer 2

To solve for the value of "x" in the equation:

2 3/5 + (x - 2 1/6) = 5 2/3

First, we'll simplify the equation step by step.

Step 1: Convert all mixed numbers to improper fractions.

2 3/5 = (5 * 2 + 3) / 5 = 13/5 2 1/6 = (6 * 2 + 1) / 6 = 13/6 5 2/3 = (3 * 5 + 2) / 3 = 17/3

Now, the equation becomes:

13/5 + (x - 13/6) = 17/3

Step 2: Remove the fractions by finding a common denominator, which in this case is 30.

Multiply every term in the equation by 30 to eliminate fractions:

30 * (13/5) + 30 * (x - 13/6) = 30 * (17/3)

Step 3: Simplify the equation further:

(30 * 13/5) + (30 * (x - 13/6)) = (30 * 17/3)

Now, calculate each term:

(6 * 13) + 30(x - 13/6) = (10 * 17)

Step 4: Continue simplifying:

78 + 30(x - 13/6) = 170

Step 5: Subtract 78 from both sides of the equation to isolate the term with "x":

30(x - 13/6) = 170 - 78 30(x - 13/6) = 92

Step 6: Divide both sides by 30 to solve for "x":

(x - 13/6) = 92 / 30

(x - 13/6) = 46/15

Step 7: Add 13/6 to both sides to isolate "x":

x = 46/15 + 13/6

Now, find a common denominator (30) and add the fractions:

x = (46/15) + (65/30)

x = (92/30) + (65/30)

x = (92 + 65) / 30

x = 157/30

So, the solution to the equation is:

x = 157/30