1. The problem states: "Twelve less than -9 times a number is equal to eight minus 4 times the number." We need to translate this into an equation and solve for the number. 2. Let the number be $x$. 3. Translate the verbal expression into an equation: - "-9 times a number" is $-9x$. - "Twelve less than -9 times a number" means subtract 12 from $-9x$, so $-9x - 12$. - "Eight minus 4 times the number" is $8 - 4x$. So the equation is: $$-9x - 12 = 8 - 4x$$ 4. Solve the equation step-by-step: Add $9x$ to both sides: $$\cancel{-9x} - 12 + 9x = 8 - 4x + 9x$$ $$-12 = 8 + 5x$$ Subtract 8 from both sides: $$-12 - 8 = 8 - 8 + 5x$$ $$-20 = 5x$$ Divide both sides by 5: $$\frac{-20}{\cancel{5}} = \frac{5x}{\cancel{5}}$$ $$-4 = x$$ 5. The solution is: $$x = -4$$ This means the number is $-4$.