Question

3/5(1/2x+1/3)=1/4x+7/24​

Answer 1

Ответ:

Пошаговое объяснение:

Answer 2

To solve the equation $\frac{3}{5} \left(\frac{1}{2}x + \frac{1}{3}\right) = \frac{1}{4}x + \frac{7}{24}$, follow these steps:

Step 1: Clear the fractions To eliminate the fractions, we can multiply both sides of the equation by the least common multiple (LCM) of the denominators. The LCM of 2, 3, and 24 is 24.

So, multiply both sides by 24:

$24 \times \left[\frac{3}{5} \left(\frac{1}{2}x + \frac{1}{3}\right)\right] = 24 \times \left[\frac{1}{4}x + \frac{7}{24}\right]$

Step 2: Simplify

On the left-hand side:

$24 \times \left[\frac{3}{5} \left(\frac{1}{2}x + \frac{1}{3}\right)\right] = 24 \times \left[\frac{3}{5} \times \frac{1}{2}x + \frac{3}{5} \times \frac{1}{3}\right]$ $= 24 \times \left[\frac{3}{10}x + \frac{1}{5}\right] = 24 \times \frac{3}{10}x + 24 \times \frac{1}{5}$ $= \frac{72}{10}x + \frac{24}{5} = \frac{36}{5}x + \frac{24}{5}$

On the right-hand side:

$24 \times \left[\frac{1}{4}x + \frac{7}{24}\right] = 24 \times \frac{1}{4}x + 24 \times \frac{7}{24}$ $= 6x + 7$

Step 3: Solve for x

Now the equation becomes:

$\frac{36}{5}x + \frac{24}{5} = 6x + 7$

Let's isolate the x term on one side and the constant term on the other:

$\frac{36}{5}x - 6x = 7 - \frac{24}{5}$

$\frac{36}{5}x - \frac{30}{5}x = \frac{35}{5}$

$\frac{6}{5}x = \frac{35}{5}$

Now, multiply both sides by the reciprocal of $\frac{6}{5}$ to solve for x:

$x = \frac{\frac{35}{5}}{\frac{6}{5}}$

$x = \frac{35}{5} \times \frac{5}{6}$

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