If (m-2,2m+1) lies on equation 2x+3y-10=0 find m

Answer

To solve the problem, we need to find the value of \( m \) such that the point \( (m-2, 2m+1) \) lies on the line defined by the equation \( 2x + 3y - 10 = 0 \).

### Step-by-step Solution:

1. **Identify the coordinates**:
The coordinates given are \( x = m - 2 \) and \( y = 2m + 1 \).

2. **Substitute the coordinates into the equation**:
We substitute \( x \) and \( y \) into the equation \( 2x + 3y - 10 = 0 \):
\[ 2(m - 2) + 3(2m + 1) - 10 = 0 \]

3. **Expand the equation**:
Now, we will expand the left-hand side:
\[ 2(m - 2) = 2m - 4 \]
\[ 3(2m + 1) = 6m + 3 \]
Therefore, substituting these back gives:
\[ 2m - 4 + 6m + 3 - 10 = 0 \]

4. **Combine like terms**:
Now, we combine all the terms:
\[ (2m + 6m) + (-4 + 3 - 10) = 0 \]
This simplifies to:
\[ 8m - 11 = 0 \]

5. **Solve for \( m \)**:
Now, we isolate \( m \):
\[ 8m = 11 \]
\[ m = \frac{11}{8} \]

### Final Answer:
The value of \( m \) is \( \frac{11}{8} \).

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