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

a different coefficient on the variable. If he sets the expressions equal to each other, will the

equation have one solution, no solution or infinitely many solutions? Use an example to support

your 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