We need to solve the linear inequality $3(1+8m) - 7(7m-3) > 49$ for $m$.

1. Problem Description

We need to solve the linear inequality $3(1+8m) - 7(7m-3) > 49$ for $m$.

2. Solution Steps

First, distribute the constants into the parentheses.

$3(1+8m) = 3 + 24m$

$-7(7m-3) = -49m + 21$

Now, substitute these back into the inequality:

$3 + 24m - 49m + 21 > 49$

Combine like terms on the left side:

$24 - 25m > 49$

Subtract 24 from both sides:

$-25m > 49 - 24$

$-25m > 25$

Divide both sides by -

2

5. Remember to flip the inequality sign when dividing by a negative number:

$m < \frac{25}{-25}$

$m < -1$

3. Final Answer

$m < -1$