Appendix A - Equations and Inequalities - Exercises - Page 416: 28

Contradiction, $\emptyset$

Step 1: $-6(2x+1)-3(x-4)=-15x+1$ Step 2: $-12x-6-3x+12=-15x+1$ Step 3: $-15x+6=-15x+1$ Step 4: Adding $15x$ to both sides, $-15x+15x+6=-15x+15x+1$ Step 5: Simplifying, $6=1$ Step 6: Since $6\ne1$, the equation is a contradiction. The solution set therefore is the empty set or null set which is characterized as $\emptyset$.