Final answer:
The equation -4b+21=11-4b simplifies to 21=11 after cancelling out the term with variable b, indicating that there is no solution as the statement is untrue.
Step-by-step explanation:
The student's question: Solve for the given variable -4b+21=11-4b.
To solve for b, we should first simplify and rearrange the equation. However, in this case we observe that the terms containing b on both sides of the equation are identical but with opposite signs, which cancels each other out. Therefore, we are left with 21=11, which is not true. This indicates that the equation has no solution; it is inconsistent because it essentially states a falsehood (21 is not equal to 11).
If b had not canceled out, or if the constants on both sides were equal, we would have been able to solve for b by isolating it on one side of the equation. However, since the terms containing b canceled out and left us with an untrue statement, it clearly shows that there is no solution for b in this equation.