The line `(3x)/5 - (2y)/3 + 1 = 0`contains the point `(m, 2m-1)`, calculate the value of m.

Answer

To find the value of \( m \) such that the point \( (m, 2m - 1) \) lies on the line given by the equation

\[ \frac{3x}{5} - \frac{2y}{3} + 1 = 0, \]

we will substitute \( x = m \) and \( y = 2m - 1 \) into the equation and solve for \( m \).

### Step 1: Substitute the point into the equation

Substituting \( x = m \) and \( y = 2m - 1 \) into the equation:

\[ \frac{3m}{5} - \frac{2(2m - 1)}{3} + 1 = 0. \]

### Step 2: Simplify the equation

Now, simplify the left-hand side:

\[ \frac{3m}{5} - \frac{4m - 2}{3} + 1 = 0. \]

### Step 3: Combine the terms

To combine the fractions, we need a common denominator. The least common multiple of 5 and 3 is 15. Thus, we rewrite each term:

\[ \frac{3m \cdot 3}{15} - \frac{(4m - 2) \cdot 5}{15} + \frac{15}{15} = 0. \]

This simplifies to:

\[ \frac{9m}{15} - \frac{20m - 10}{15} + \frac{15}{15} = 0. \]

### Step 4: Combine the fractions

Now, combine the fractions:

\[ \frac{9m - (20m - 10) + 15}{15} = 0. \]

This simplifies to:

\[ \frac{9m - 20m + 10 + 15}{15} = 0. \]

### Step 5: Simplify further

Combine like terms:

\[ \frac{-11m + 25}{15} = 0. \]

### Step 6: Solve for \( m \)

To eliminate the fraction, multiply both sides by 15:

\[ -11m + 25 = 0. \]

Rearranging gives:

\[ -11m = -25 \implies m = \frac{25}{11}. \]

### Step 7: Convert to mixed fraction

To convert \( \frac{25}{11} \) to a mixed fraction, divide 25 by 11:

\[ 25 \div 11 = 2 \quad \text{(remainder 3)}. \]

Thus,

\[ \frac{25}{11} = 2 \frac{3}{11}. \]

### Final Answer

The value of \( m \) is

\[ \frac{25}{11} \quad \text{or} \quad 2 \frac{3}{11}. \]

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