Let's solve the equation step by step:

Given equation:

$6(4x + 5) = 3x - 4(-4x - 1) + 5$

Step 1: Expand both sides.

Expand the terms on both sides of the equation:

• Left-hand side: $6(4x + 5) = 6 \cdot 4x + 6 \cdot 5 = 24x + 30$

• Right-hand side: $-4(-4x - 1) = -4 \cdot -4x - 4 \cdot -1 = 16x + 4$ So, the right-hand side becomes: $3x + 16x + 4 + 5 = 19x + 9$

Step 2: Write the expanded equation.

$24x + 30 = 19x + 9$

Step 3: Isolate $x$.

Move all terms involving $x$ to one side and constant terms to the other side:

$24x - 19x = 9 - 30$

This simplifies to: $5x = -21$

Step 4: Solve for $x$.

$x = \frac{-21}{5}$

So, the solution is: $x = -\frac{21}{5}$

Would you like more details on any of the steps or further clarification?

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Here are 5 related questions you might find interesting:

1. How would the solution change if the signs in front of the constants were different?
2. How can you check if the solution is correct by plugging it back into the original equation?
3. What happens if you add a fraction in the equation?
4. How would the process differ if the equation involved quadratic terms?
5. Can you solve similar problems with inequalities instead of equalities?

Tip: When solving equations, always expand and simplify both sides first before moving terms around.