Question

11. Isaac wrote two simplified expressions that were not equal to each other. Each equation also had

Answer 1

Answer:

The equation has only one solution

Step-by-step explanation:

* Lets explain how to solve the problem

- There are three types of solutions for the equations

Case (1)

# Two sides of the equation have different coefficient of the variable

   and same or different numerical terms, then the equation has only

   one solution

- Ex: 2x + 5 = x + 5, lets solve it

∵ 2x + 5 = x + 5

- subtract x from both sides

∴ x + 5 = 5

- Subtract 5 from both sides

∴ x = 0

- Zero is a solution

∴ The solution of the equation is x = 0

- If the numerical terms are different x will be any other value, so the

 equation has only one solution

∴ The equation has one solution

Case (2)

# Two sides of the equation have same coefficient of the variable,

  and different numerical terms, then the equation has no solution

- Ex: 14x - 20 = 14x + 10, lets solve it

∵ 14x - 20 = 14x + 10

- Subtract 14x from both sides

∴ - 20 = 10

- The left hand side not equal the right hand side , then there is

  no value of x can make the two sides equal

∴ The equation has no solution

Case (3)

# Two sides of the equation have same coefficient of the variable,

  and same numerical terms, then the equation has infinitely

  many solutions

- Ex: 3x + 5 = 3x + 5, lets solve it

∵ 3x + 5 = 3x + 5

- Subtract 3x from both sides

∴ 5 = 5

- The left hand side is equal to the right hand side , then x can be

  any value because the two sides is already equal without x

∴ The equation has infinitely many solutions

∵ He will write two expressions simplified , not equal , have different

  coefficients on the variables and equate them, then it is like

  the first case

- That means not same coefficient of the variable, and may be not

 same numerical term

∴ The equation has only one solution