Inequality Solve B16522

1. **State the problem:** Solve the inequality $$-6(7 - 3x) > 12$$ and graph the solution. 2. **Apply the distributive property:** Multiply $$-6$$ by each term inside the parentheses. $$-6 \times 7 = -42$$ $$-6 \times (-3x) = +18x$$ So the inequality becomes: $$-42 + 18x > 12$$ 3. **Isolate the variable term:** Add $$42$$ to both sides to move constants to the right. $$-42 + 18x + 42 > 12 + 42$$ $$18x > 54$$ 4. **Divide both sides by 18:** $$\frac{18x}{\cancel{18}} > \frac{54}{\cancel{18}}$$ $$x > 3$$ 5. **Interpret the solution:** The solution to the inequality is all $$x$$ values greater than $$3$$. 6. **Graph the solution:** - Draw a number line. - Mark the point $$3$$. - Since the inequality is strict ($$>$$), use an open circle at $$3$$. - Shade the number line to the right of $$3$$ to indicate all values greater than $$3$$. **Final answer:** $$x > 3$$