Solve the following eqations.Check your result in each case
`(2m+5)=3m-10`

Answer

To solve the equation \( (2m + 5) = (3m - 10) \), we will follow these steps:

### Step 1: Write down the equation
The given equation is:
\[ 2m + 5 = 3m - 10 \]

### Step 2: Move the variable terms to one side
To isolate the variable \( m \), we can move the term \( 3m \) from the right side to the left side. When we do this, we change its sign from positive to negative:
\[ 2m - 3m + 5 = -10 \]

### Step 3: Simplify the equation
Now, simplify the left side:
\[ (2m - 3m) + 5 = -10 \]
This simplifies to:
\[ -m + 5 = -10 \]

### Step 4: Move the constant term to the other side
Next, we will move the constant term \( 5 \) from the left side to the right side. When we do this, we change its sign from positive to negative:
\[ -m = -10 - 5 \]

### Step 5: Simplify the right side
Now, simplify the right side:
\[ -m = -15 \]

### Step 6: Solve for \( m \)
To find \( m \), we multiply both sides by -1:
\[ m = 15 \]

### Step 7: Check the result
To verify our solution, we will substitute \( m = 15 \) back into the original equation:
- Left side:
\[ 2m + 5 = 2(15) + 5 = 30 + 5 = 35 \]
- Right side:
\[ 3m - 10 = 3(15) - 10 = 45 - 10 = 35 \]
Since both sides are equal, \( 35 = 35 \), our solution is confirmed.

### Final Answer:
\[ m = 15 \]

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