a Linear equation may have one solution, no solution or indefinitely many solutions. To determine how many solutions the given equation has, we will solve it.
b Linear equation may have one solution, no solution or indefinitely many solutions. To determine how many solutions the given equation has, we will solve it.
3(x-4)-x=5+2x
To solve an equation, we should first gather all of the variable terms on one side of the equation and all of the constant terms on the other side using the Properties of Equality. In this case, we need to start by using the Distributive Property to simplify the left-hand side of the equation.
Simplifying the equation resulted in a contradiction. Thus, the given equation has no solution.
cQuadratic equations may have one solution, two solutions, or no solution. To determine how many solutions the given equation has, we will solve it. Since the equation is already given in the factored form, we can do it using the Zero Product Property.
Using the Zero Product Property we found that the equation has two solutions.
d Quadratic equations may have one solution, two solutions, or no solution. To determine how many solutions the given equation has, we will solve it. To do this, we can start by using factoring and then we will use the Zero Product Property.
Factoring
We want to factor the given equation. Factoring is much easier when our polynomial is a perfect square trinomial. To determine if the expression on the left-hand side of the equation is a perfect square trinomial, we need to ask ourselves three questions.
Is the first term a perfect square?
x^2= x^2 âś“
Is the last term a perfect square?
4= 2^2 âś“
Is the middle term twice the product of 2 and x?
4x=2* 2* x âś“
As we can see, the answer to all three questions is yes! Therefore, we can write the trinomial as the square of a binomial. Note there is a subtraction sign in the middle.
x^2-4x+4=0 ⇔ ( x- 2)^2=0
Zero Product Property
Since the equation is already written in factored form, we can now use the Zero Product Property.
