1. **State the problem:** Solve each equation for the variable. 2. **Equation 1:** $x - 3 = 11$ - Add 3 to both sides: $$x - 3 + 3 = 11 + 3$$ $$x = 14$$ 3. **Equation 2:** $\frac{1}{4} = 10$ - This is a false statement since $\frac{1}{4}$ is not equal to 10. - No solution. 4. **Equation 3:** $\frac{t}{6} = 2$ - Multiply both sides by 6: $$\cancel{6} \times \frac{t}{\cancel{6}} = 2 \times 6$$ $$t = 12$$ 5. **Equation 4:** $2x = 10$ - Divide both sides by 2: $$\frac{2x}{\cancel{2}} = \frac{10}{\cancel{2}}$$ $$x = 5$$ 6. **Equation 5:** $x + 6 = 15$ - Subtract 6 from both sides: $$x + 6 - 6 = 15 - 6$$ $$x = 9$$ 7. **Equation 6:** $4x = 12$ - Divide both sides by 4: $$\frac{4x}{\cancel{4}} = \frac{12}{\cancel{4}}$$ $$x = 3$$ **Final answers:** - $x = 14$ - No solution - $t = 12$ - $x = 5$ - $x = 9$ - $x = 3$