Final answer:
Through substitution and the transitive property of equality, we can use the given equations to algebraically prove that x equals v.
Step-by-step explanation:
The algebraic proof to show that x = v is based on the given equations x * y = z, w * v = z, and w = z. By equating the expressions for z since they are equal to each other, we can set up a chain of equalities because the values on the left-hand side must also be equal. Since w is equal to z, we can substitute w for z in any of the equations. Then, by transitive property, we can deduce that x * y = w * v and with w = z, we further simplify to x * y = z * v. If we divide both sides by y, assuming y is not zero, we get x = v.
Therefore, with the knowledge that w = z and the two products that equal z, we can conclude through substitution and simplification that x is indeed equal to v..