Question

(X-2 7/8)+3 5/6=4 2/3

Answer 1

Х-2 7/8+3 5/6=4 2/3
х=2 7/8-3 5/6-4 2/3
х=-5 5/8

Answer 2

To solve the equation $(X - 2 \frac{7}{8}) + 3 \frac{5}{6} = 4 \frac{2}{3}$, follow these steps:

Step 1: Convert the mixed numbers to improper fractions. Step 2: Perform the operations. Step 3: Convert the result back to a mixed number (if needed).

Step 1: Convert the mixed numbers to improper fractions. $2 \frac{7}{8}$ as an improper fraction is $\frac{23}{8}$. $3 \frac{5}{6}$ as an improper fraction is $\frac{23}{6}$.

Step 2: Perform the operations. $(X - \frac{23}{8}) + \frac{23}{6} = 4 \frac{2}{3}$

Step 3: To combine the fractions on the left side, find a common denominator. The common denominator for 8 and 6 is 24.

$\frac{3}{24}X - \frac{69}{24} + \frac{92}{24} = 4 \frac{2}{3}$

Combine the fractions on the left side:

$\frac{3}{24}X + \frac{23}{24} = 4 \frac{2}{3}$

Now, let's convert the mixed number on the right side to an improper fraction:

$4 \frac{2}{3}$ as an improper fraction is $\frac{14}{3}$.

The equation becomes:

$\frac{3}{24}X + \frac{23}{24} = \frac{14}{3}$

Now, we need to isolate $X$ on one side of the equation. To do that, we'll eliminate the fraction on the left side by multiplying both sides by the common denominator, which is 24:

$24 \cdot \left(\frac{3}{24}X + \frac{23}{24}\right) = 24 \cdot \frac{14}{3}$

Simplifying:

$3X + 23 = \frac{112}{3}$

Next, let's isolate $X$ by moving the constant term (23) to the other side. Subtract 23 from both sides:

$3X = \frac{112}{3} - 23$

To subtract the fractions, find a common denominator, which is 3:

$3X = \frac{112}{3} - \frac{69}{3}$

$3X = \frac{43}{3}$

Finally, divide by 3 to solve for $X$:

$X = \frac{43}{3} \div 3$

$X = \frac{43}{3} \cdot \frac{1}{3}$

$X = \frac{43}{9}$

To convert the improper fraction $\frac{43}{9}$ back to a mixed number:

Divide the numerator (43) by the denominator (9):

$43 \div 9 = 4$ with a remainder of 7.

The mixed number is $4 \frac{7}{9}$.

So, the solution to the equation is $X = 4 \frac{7}{9}$.