To solve the equation:

$-4(6x - 4) = -(4x - 6) + 30$

Let's follow the steps to find $x$.

Step 1: Expand both sides

First, expand both sides of the equation.

$-4(6x - 4) = -4(6x) + (-4)(-4) = -24x + 16$ $-(4x - 6) = -4x + 6$

So the equation becomes:

$-24x + 16 = -4x + 6 + 30$

Step 2: Simplify the right-hand side

Now, simplify the right-hand side by combining like terms:

$-24x + 16 = -4x + 36$

Step 3: Move all terms involving $x$ to one side

Add $24x$ to both sides to move the $x$-terms to one side:

$16 = 20x + 36$

Step 4: Isolate the $x$-term

Subtract 36 from both sides to isolate the term with $x$:

$16 - 36 = 20x$ $-20 = 20x$

Step 5: Solve for $x$

Now, divide both sides by 20:

$x = \frac{-20}{20} = -1$

Final Answer:

$x = -1$

Would you like further details on any of the steps or have any questions?

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Here are 5 related questions for further practice:

1. Solve for $x$: $3(2x - 5) = 2(x + 6)$
2. Solve for $x$: $-5(3x + 1) = 15x - 10$
3. Solve $7x - 4(2x + 5) = -3$
4. Solve $2(5x + 3) = x + 17$
5. Solve $6x + 3 = 2(3x - 5) + 13$

Tip: Always distribute multiplication before combining like terms in equations for easier solving.