Subjects algebra

Linear Equation D73029

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1. **State the problem:** Solve the equation $5 - 6(2x + 2) = -2(6x + 5) + 4$ using the method of drawing a vertical line under the equal sign to keep both sides balanced. 2. **Distribute the terms:** Left side: $5 - 6(2x + 2) = 5 - 12x - 12$ Right side: $-2(6x + 5) + 4 = -12x - 10 + 4$ 3. **Simplify both sides:** Left side: $5 - 12 = -7$, so $-7 - 12x$ Right side: $-10 + 4 = -6$, so $-12x - 6$ 4. **Rewrite the equation with simplified expressions:** $$-7 - 12x = -12x - 6$$ 5. **Draw a vertical line under the equal sign to keep balance and start isolating terms:** Subtract $-12x$ from both sides: $$-7 - 12x - \cancel{-12x} = -12x - 6 - \cancel{-12x}$$ which simplifies to: $$-7 = -6$$ 6. **Analyze the result:** Since $-7 \neq -6$, this means the equation has no solution. **Final answer:** There is no solution to the equation because it leads to a contradiction.