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
<u>Case (1)</u>
# Two sides of the equation have <u><em>different coefficient of the variable</em></u>
and <u><em>same or different numerical terms</em></u>, 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
- <em>If the numerical terms are different x will be any other value, so the</em>
<em> equation has only one solution</em>
∴ The equation has one solution
<u>Case (2)</u>
# Two sides of the equation have <u><em>same coefficient of the variable</em></u>,
and <u><em>different numerical terms</em></u>, 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
<u>Case (3)</u>
# Two sides of the equation have <u><em>same coefficient of the variable</em></u>,
and <u><em>same numerical terms</em></u>, 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
