Question

1 2/3x-1 4/21=2 1/7 1 2/3x-1 4/21x=2 1/7

Answer 1

Х=37
    ---
    42
х=9
    ---
    10

∅

Answer 2

To solve the equation $1\frac{2}{3}x - \frac{1}{4} = 2\frac{1}{7}\left(1\frac{2}{3}x - \frac{1}{21}\right)$, you can follow these steps:

Step 1: Distribute the $2\frac{1}{7}$ on the right side of the equation:

$1\frac{2}{3}x - \frac{1}{4} = 2\frac{1}{7} \cdot 1\frac{2}{3}x - 2\frac{1}{7} \cdot \frac{1}{21}$

Step 2: Simplify the fractions on the right side:

$1\frac{2}{3}x - \frac{1}{4} = \frac{15}{7}x - \frac{1}{7}$

Step 3: Move all terms containing $x$ to one side of the equation and constants to the other side:

$1\frac{2}{3}x - \frac{15}{7}x = \frac{1}{7} + \frac{1}{4}$

Step 4: Find a common denominator and add the fractions on the right side:

$\frac{7}{3}x - \frac{15}{7}x = \frac{4 + 3}{28}$

Step 5: Combine like terms on both sides:

$\frac{7}{3}x - \frac{15}{7}x = \frac{7}{28}$

Step 6: Find a common denominator on the left side:

$\frac{28}{21}x - \frac{15}{7}x = \frac{7}{28}$

Step 7: Subtract the fractions on the left side:

$\frac{28}{21}x - \frac{15}{7}x = \frac{7}{28}$

$\frac{28}{21}x - \frac{60}{21}x = \frac{7}{28}$

Step 8: Combine like terms on the left side:

$\frac{28 - 60}{21}x = \frac{7}{28}$

Step 9: Simplify the left side:

$-\frac{32}{21}x = \frac{7}{28}$

Step 10: Divide both sides by $-\frac{32}{21}$ to isolate $x$:

$x = \frac{7}{28} \div \left(-\frac{32}{21}\right)$

To divide fractions, multiply the first fraction by the reciprocal of the second fraction:

$x = \frac{7}{28} \cdot \left(-\frac{21}{32}\right)$

Now, multiply the numerators and denominators:

$x = \frac{(7 \cdot -21)}{(28 \cdot 32)}$

$x = \frac{-147}{896}$