Question

5/8× (2 1/6+x)= 7/8​

Answer 1

Ответ:

$-\frac{23}{30}$

Пошаговое объяснение:

$\frac{5}{8} *(2\frac{1}{6} +x)=\frac{7}{8} \\\frac{13}{6} +x=\frac{7}{8} /\frac{5}{8} =\frac{7}{8} *\frac{8}{5} =\frac{7}{5} \\x=\frac{7}{5} -\frac{13}{6} =\frac{42}{30}-\frac{65}{30} =-\frac{23}{30}$

Answer 2

To solve the equation $\frac{5}{8} \times \left(2 \frac{1}{6} + x\right) = \frac{7}{8}$, you can follow these steps:

Step 1: Convert the mixed number $2 \frac{1}{6}$ to an improper fraction.

$2 \frac{1}{6} = \frac{2 \times 6 + 1}{6} = \frac{13}{6}$

So, the equation becomes:

$\frac{5}{8} \times \left(\frac{13}{6} + x\right) = \frac{7}{8}$

Step 2: Distribute $\frac{5}{8}$ to both terms inside the parentheses.

$\frac{5}{8} \times \frac{13}{6} + \frac{5}{8} \times x = \frac{7}{8}$

Step 3: Multiply the fractions on the left side.

$\frac{5 \cdot 13}{8 \cdot 6} + \frac{5}{8}x = \frac{7}{8}$

$\frac{65}{48} + \frac{5}{8}x = \frac{7}{8}$

Step 4: Subtract $\frac{65}{48}$ from both sides to isolate $x$.

$\frac{5}{8}x = \frac{7}{8} - \frac{65}{48}$

Step 5: Find a common denominator and subtract the fractions on the right side.

To find a common denominator between 8 and 48, you can use 48. So, convert $\frac{7}{8}$ to have a denominator of 48:

$\frac{7}{8} = \frac{7 \cdot 6}{8 \cdot 6} = \frac{42}{48}$

Now, subtract:

$\frac{5}{8}x = \frac{42}{48} - \frac{65}{48}$

Step 6: Subtract the fractions on the right side.

$\frac{5}{8}x = \frac{42 - 65}{48}$

$\frac{5}{8}x = \frac{-23}{48}$

Step 7: Divide both sides by $\frac{5}{8}$ to solve for $x$.

$x = \frac{-23}{48} \div \frac{5}{8}$

To divide by a fraction, multiply by its reciprocal:

$x = \frac{-23}{48} \times \frac{8}{5}$

Now, multiply the numerators and denominators:

$x = \frac{-23 \cdot 8}{48 \cdot 5} = \frac{-184}{240}$

Reduce the fraction by finding the greatest common divisor (GCD) of 184 and 240, which is 8:

$x = \frac{-23 \cdot (8/8)}{30 \cdot (8/8)}$

$x = \frac{-23 \cdot 1}{30 \cdot 1}$