Question

4 3/5+(x-2 5/6)=5 2/3​

Answer 1

Ответ:

$4\frac{3}{5}+(x-2\frac{5}{6})=5\frac{2}{3}\\\frac{23}{5}+x-\frac{17}{6} =\frac{17}{3} \\\frac{138}{30}-\frac{85}{30}+x=\frac{170}{30} \\\frac{53}{30}+x=\frac{170}{30}\\x=\frac{170}{30}-\frac{53}{30}\\x=\frac{117}{30}\\x=3\frac{27}{30}\\x= 3\frac{9}{10}$

Пошаговое объяснение:

Answer 2

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

Step 1: Convert all mixed numbers to improper fractions. $4 \frac{3}{5}$ becomes $\frac{4 \cdot 5 + 3}{5} = \frac{23}{5}$. $2 \frac{5}{6}$ becomes $\frac{2 \cdot 6 + 5}{6} = \frac{17}{6}$. $5 \frac{2}{3}$ becomes $\frac{5 \cdot 3 + 2}{3} = \frac{17}{3}$.

So, the equation becomes $\frac{23}{5} + (x - \frac{17}{6}) = \frac{17}{3}$.

Step 2: Simplify the equation by getting rid of fractions. You can do this by multiplying each term in the equation by the least common multiple (LCM) of the denominators, which is 30 in this case.

Multiply each term by 30:

$30 \cdot \frac{23}{5} + 30 \cdot (x - \frac{17}{6}) = 30 \cdot \frac{17}{3}$.

Now, simplify each term:

$138 + 30x - 85 = 170$.

Step 3: Combine like terms.

$30x + 138 - 85 = 170$.

$30x + 53 = 170$.

Step 4: Isolate the variable $x$. Subtract 53 from both sides of the equation:

$30x = 170 - 53$.

$30x = 117$.

Step 5: Solve for $x$ by dividing both sides by 30:

$x = \frac{117}{30}$.

Step 6: Simplify the fraction, if possible. The greatest common divisor (GCD) of 117 and 30 is 3, so you can simplify the fraction:

$x = \frac{117 \div 3}{30 \div 3}$.

$x = \frac{39}{10}$.

So, the solution to the equation is $x = \frac{39}{10}$, which is equivalent to $x = 3.9$.