1. **State the problem:** Solve the inequality $$\frac{1}{7}(42x + 28) < 28$$ to find the values of $x$ that satisfy it. 2. **Use the distributive property:** Multiply both sides by 7 to eliminate the fraction. $$\cancel{7} \times \frac{1}{\cancel{7}}(42x + 28) < 28 \times 7$$ This simplifies to: $$42x + 28 < 196$$ 3. **Isolate the variable term:** Subtract 28 from both sides. $$42x + 28 - 28 < 196 - 28$$ $$42x < 168$$ 4. **Solve for $x$:** Divide both sides by 42. $$\frac{42x}{\cancel{42}} < \frac{168}{\cancel{42}}$$ $$x < 4$$ **Final answer:** $$x < 4$$ --- 1. **State the problem:** Find the value of $x$ satisfying $$-3x + 2 < 14$$. 2. **Isolate the variable term:** Subtract 2 from both sides. $$-3x + 2 - 2 < 14 - 2$$ $$-3x < 12$$ 3. **Solve for $x$:** Divide both sides by -3 and remember to reverse the inequality sign because dividing by a negative number flips the inequality. $$\frac{-3x}{\cancel{-3}} > \frac{12}{\cancel{-3}}$$ $$x > -4$$ 4. **Interpret the solution:** $x$ must be greater than $-4$. Among the options (-3, -4, -5, -6), the values satisfying $x > -4$ are $-3$ only. **Final answer:** $x = -3$