Question

2 1/3(3/7x+9/14)=5 1/3 (1/24-3x)

Answer 1

$x = - \frac{23}{306}$

альтернативный вид

x≈0.0751634

Answer 2

To solve the equation $2 \frac{1}{3}\left(\frac{3}{7}x + \frac{9}{14}\right) = 5 \frac{1}{3}\left(\frac{1}{24} - 3x\right)$, you can follow these steps:

Step 1: Distribute the fractions on both sides of the equation to eliminate the fractions. To do this, multiply both sides of the equation by the common denominator of all the fractions involved, which is 168.

$2 \frac{1}{3} \cdot 168 \left(\frac{3}{7}x + \frac{9}{14}\right) = 5 \frac{1}{3} \cdot 168 \left(\frac{1}{24} - 3x\right)$

Simplify the fractions and multiply by 168:

$\left(\frac{2}{3}\right) \cdot 168 \left(\frac{3}{7}x + \frac{9}{14}\right) = \left(\frac{5}{3}\right) \cdot 168 \left(\frac{1}{24} - 3x\right)$

Step 2: Continue simplifying:

$112 \left(\frac{3}{7}x + \frac{9}{14}\right) = 280 \left(\frac{1}{24} - 3x\right)$

Step 3: Distribute the constants and fractions on both sides of the equation:

$\frac{112 \cdot 3}{7}x + \frac{112 \cdot 9}{14} = \frac{280}{24} - 280 \cdot 3x$

Now, simplify the fractions:

$\frac{336}{7}x + \frac{1008}{14} = \frac{280}{24} - 840x$

Step 4: Simplify further:

$48x + 72 = 35 - 840x$

Step 5: Move all the terms involving $x$ to one side of the equation and the constants to the other side:

$48x + 840x = 35 - 72$

Step 6: Combine like terms:

$888x = -37$

Step 7: Finally, solve for $x$ by dividing both sides by 888:

$x = \frac{-37}{888}$

So, the solution to the equation is $x = \frac{-37}{888}$.