Question: Solve for x:
5x - 2(0.1x - 1) = 7.2 - 4.4(-x - 6)
1. **State the problem:** Solve the equation $$5x - 2(0.1x - 1) = 7.2 - 4.4(-x - 6)$$ for $$x$$.
2. **Apply the distributive property:**
$$5x - 2 \times 0.1x + 2 \times 1 = 7.2 - 4.4 \times (-x) - 4.4 \times (-6)$$
which simplifies to
$$5x - 0.2x + 2 = 7.2 + 4.4x + 26.4$$
3. **Combine like terms on each side:**
Left side: $$5x - 0.2x = 4.8x$$
Right side: $$7.2 + 26.4 = 33.6$$
So the equation becomes
$$4.8x + 2 = 4.4x + 33.6$$
4. **Isolate variable terms on one side and constants on the other:**
Subtract $$4.4x$$ from both sides:
$$4.8x - \cancel{4.4x} + 2 = \cancel{4.4x} + 33.6 - 4.4x$$
which simplifies to
$$0.4x + 2 = 33.6$$
Subtract $$2$$ from both sides:
$$0.4x + \cancel{2} - 2 = 33.6 - \cancel{2}$$
which simplifies to
$$0.4x = 31.6$$
5. **Solve for $$x$$ by dividing both sides by $$0.4$$:**
$$x = \frac{31.6}{0.4}$$
Use the cancellation notation:
$$x = \frac{31.6}{\cancel{0.4}} \times \frac{\cancel{1}}{1}$$
Calculate the division:
$$x = 79$$
**Final answer:** $$x = 79$$