Question

Solve the equation a-15=25 and state the axiom used.

Answer 1

HINT: The Greek mathematicians of Euclid’s time thought of geometry as an abstract model of the worlds in which they lived.

Complete step-by-step answer:

Some of Euclid’s axioms are given below:

(1) Things which are equal to the same thing are equal to one another.

Example: For example, if an area of a triangle equals the area of a rectangle and the area of the rectangle equals that of a square, then the area of the triangle also equals the area of the square.


(2) If equals are added to equals, the holes are equal.

Example: For example, a line cannot be added to a rectangle, nor can an angle be compared to a pentagon.


(3) If equals are subtracted from equals, the remainders are equal.

Example: For example, a line cannot be subtracted to a rectangle, nor can an angle be compared to a pentagon.


(4) Things which coincide with one another are equal to one another.

Example: Segment AB = Segment BA; ∠A = ∠A.


(5) The whole is greater than the part.

Example: If a quantity B is a part of another quantity A, then A can be written as the sum of B and some third quantity C. Symbolically, A > B means that there is some C such that A = B + C.


(6) Things which are double of the same things are equal to one another.

Example: If 2x = 2y then x = y.


(7) Things which are halves of the same things are equal to one another.

Example: If \[\dfrac{1}{2}x=\dfrac{1}{2}y\] then x = y.


As mentioned in the question, we have to find the solution of the given equation and also state the axiom that is used.

Now, let us consider the equation as follows

a-15=25

Now, we can solve it as follows

a-15+15=25+15

a=40

Hence, the solution of the equation is 40 and the axiom that is used to solve this question is the second axiom which states that if equals are added to equals, the holes are equal.

NOTE: The students can make an error if they don’t know about the axioms and postulates of Euclid because without knowing these it would be very difficult for them to get to the correct answer.
Also, knowing about axioms and postulates can also help the students to visualize every question differently.