Let's solve the equation step by step:

Given equation:

$4(-2x + 4) = -10(x - 6)$

Step 1: Distribute the constants on both sides.

Distribute the 4 on the left side, and the -10 on the right side:

$4 \times -2x + 4 \times 4 = -10 \times x + (-10) \times (-6)$ $-8x + 16 = -10x + 60$

Step 2: Get all the $x$-terms on one side and constant terms on the other side.

Add $10x$ to both sides to move all $x$-terms to the left: $-8x + 10x + 16 = 60$ $2x + 16 = 60$

Step 3: Move the constant terms.

Subtract 16 from both sides to isolate the term with $x$: $2x = 60 - 16$ $2x = 44$

Step 4: Solve for $x$.

Divide both sides by 2: $x = \frac{44}{2}$ $x = 22$

Final Answer:

$x = 22$

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Would you like further clarification or details on any step? Here are some related questions you can explore:

1. How do you solve equations with fractions or decimals?
2. What are other methods to solve linear equations, such as using substitution or elimination?
3. What is the distributive property and how is it applied in algebra?
4. How do you check if a solution to an equation is correct?
5. How do you solve equations with parentheses on both sides?

Tip: Always simplify both sides of the equation as much as possible before isolating the variable to make solving easier.