Solve:`(3x)/10+(2x)/5=(7x)/25+29/25`

Answer

To solve the equation \(\frac{3x}{10} + \frac{2x}{5} = \frac{7x}{25} + \frac{29}{25}\), we will follow these steps:

### Step 1: Find a common denominator for the fractions on the left side.
The denominators are 10 and 5. The least common multiple (LCM) of 10 and 5 is 10.

### Step 2: Rewrite the fractions with the common denominator.
\[ \frac{3x}{10} + \frac{2x}{5} = \frac{3x}{10} + \frac{2 \cdot 2x}{2 \cdot 5} = \frac{3x}{10} + \frac{4x}{10} = \frac{3x + 4x}{10} = \frac{7x}{10} \]

### Step 3: Rewrite the right side.
The right side has \(\frac{7x}{25} + \frac{29}{25}\). Since both fractions have the same denominator, we can combine them:
\[ \frac{7x + 29}{25} \]

### Step 4: Set the two sides equal to each other.
Now we have:
\[ \frac{7x}{10} = \frac{7x + 29}{25} \]

### Step 5: Cross-multiply to eliminate the fractions.
Cross-multiplying gives us:
\[ 7x \cdot 25 = 10 \cdot (7x + 29) \]
This simplifies to:
\[ 175x = 70x + 290 \]

### Step 6: Move all terms involving \(x\) to one side.
Subtract \(70x\) from both sides:
\[ 175x - 70x = 290 \]
This simplifies to:
\[ 105x = 290 \]

### Step 7: Solve for \(x\).
Divide both sides by 105:
\[ x = \frac{290}{105} \]

### Step 8: Simplify the fraction.
To simplify \(\frac{290}{105}\), we can find the greatest common divisor (GCD) of 290 and 105, which is 5:
\[ x = \frac{290 \div 5}{105 \div 5} = \frac{58}{21} \]

### Final Answer:
Thus, the solution to the equation is:
\[ \boxed{\frac{58}{21}} \]