12(х+1 1/3)=5(21/5х+7 4/15)

Let's solve the equation step by step:

The equation is:

\[ 12\left(x + \frac{4}{3}\right) = 5\left(\frac{21}{5}x + \frac{109}{15}\right) \]

1. Convert mixed numbers to improper fractions: \[ 1\frac{1}{3} = \frac{4}{3} \] \[ 7\frac{4}{15} = \frac{7 \times 15 + 4}{15} = \frac{105 + 4}{15} = \frac{109}{15} \]

2. Substituting these values back into the equation: \[ 12\left(x + \frac{4}{3}\right) = 5\left(\frac{21}{5}x + \frac{109}{15}\right) \]

3. Distribute on both sides:

   • Left side: \[ 12x + 12 \cdot \frac{4}{3} = 12x + 16 \]

   • Right side: \[ 5 \cdot \frac{21}{5}x + 5 \cdot \frac{109}{15} = 21x + \frac{545}{15} \] To simplify \(\frac{545}{15}\): \[ \frac{545 \div 5}{15 \div 5} = \frac{109}{3} \]

So now our equation looks like this: \[ 12x + 16 = 21x + \frac{109}{3} \]

4. Combine like terms: To get rid of the fraction, let's first multiply every term by 3: \[ 3(12x) + 3(16) = 3(21x) + 109 \] \[ 36x + 48 = 63x + 109 \]

5. Move all terms involving \(x\) to one side and constant terms to the other side: \[ 36x - 63x = 109 - 48 \] \[ -27x = 61 \]

6. Divide by -27: \[ x = -\frac{61}{27} \]

Thus, the solution to the equation \(12(x + 1 \frac{1}{3}) = 5(21/5x + 7 \frac{4}{15})\) is: \[ x = -\frac{61}{27} \]