A teacher asks the class to construct their own linear equation in one variable that…
MATHEMATICS · Multi-part · CBSE · Mathematics · Algebra Play · Algebra Play
Problem
A teacher asks the class to construct their own linear equation in one variable that satisfies the following conditions:
• The solution of the equation must be 4.
• The coefficient of x must be a non-zero multiple of 3.
• The constant term must be a negative two-digit integer.
(i) Let the coefficient of x be 3k, where k is a non-zero integer, and let the constant term be b. Using the fact that the solution is 4, derive an expression for the right–hand side of the equation 3kx+b=c.
(ii) Taking k=−2 and b=−14, write one specific equation satisfying all the above conditions. Solve this equation to verify that its solution is indeed 4.
(iii) Explain briefly why infinitely many different linear equations can be constructed that meet the stated conditions.