We can check our answer by substituting it back into the original equation. If simplifying the equation results in a true statement, we will know that our answer is correct. Let's do it!
ax^2+ bx+ c=0 ⇕ x=- b± sqrt(b^2-4 a c)/2 a
Since the equation is already written in the correct form, we can identify the values of a, b, and c.
2x^2-9x-5=0 ⇕ 2x^2+( - 9)x+( - 5)=0We see that a= 2, b= - 9, and c= - 5. Let's substitute these values into the Quadratic Formula.
Again, since the left-hand side is equal to the right-hand side, our solution is correct.
c To solve the proportion, we will start by using the Cross Products Property. Remember that we will need to treat both the 5x-1 and x+1 as single quantities in the cross multiplication process.
3/5x-1=1/x+1
⇔
3(x+1)=5x-1
From here, we will continue solving for x by using the Distributive Property and the Properties of Equality.
Notice that we have x-terms in the denominators of our proportion. When solving this type equation, it is important to check for extraneous solutions. We can do so by substituting our solution into the original equation and simplifying. If the result is a true statement, our answer is correct.
|2x-1|= 5
This equation means that the distance is 5, either in the positive direction or the negative direction.
|2x-1|= 5 ⇒ l2x-1= 5 2x-1= - 5
To find the solutions to the absolute value equation, we need to solve both of these cases for x.
Both 3 and -2 are solutions to the absolute value equation.
Checking Our Answers
When solving an absolute value equation, it is important to check for extraneous solutions. We can check our answers by substituting them back into the original equation. Let's start with x=3.
