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 the variable term is in denominator, so we will start by multiplying the equation by x to eliminate fractions.
Since the left-hand side is equal to the right-hand side, our solution is correct.
b
To solve equations with a variable expression inside a radical, we first want to make sure the radical is isolated. Then we can raise both sides of the equation to a power equal to the index of the radical.
Let's try to solve our equation using this method!
We found that x=± 5. Thus, there are two solutions for the equation, which are x=5 and x=- 5. We can check our solutions by substituting them into the original equation. We will start with x=5.
Again, we created a true statement. x=- 5 is indeed a solution of the equation.
d
Inequalities can be solved in the same way as equations, by performing inverse operations on both sides until the variable is isolated. The only difference is that when you divide or multiply by a negative number, you must reverse the inequality sign.
This inequality tells us that all values greater than 5 will satisfy the inequality. Now, we can check our solution by substituting three values of x into the original inequality.
Value of x
Substitute
Simplify
4
2( 4-3) ? > 4
2 ≯ 4
5
2( 5-3) ? > 4
4 ≯ 4
6
2( 6-3) ? > 4
6 > 4
As we can see, values of x greater than 5 are indeed the solution of the given inequality.
