Chapter Test
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When you solve the inequality, make sure you consider that the radicand has to be non-negative.
Solution inequality: 3≤ x≤ 12
Solution equality: x=12
Similarities and differences: See solution.
To solve the inequality, we have to perform inverse operations until x is isolated.
The solutions to the inequality is x≤ 12. However, we also have to consider the fact that our variable, x, is underneath a radical with an even index. This means x is also limited to numbers that makes the radical's argument non-negative.
To solve the equality, we also have to perform inverse operations until x is isolated.
The solution to the equality is x= 12.
Notice that we solved the equation and inequality in the same way, by performing inverse operations until x was isolated. This is the similarity between solving radical equations and radical inequalities.
The difference lies in their solutions. For an equation, the solution is a number while for an inequality, the solution is a range of numbers. Also, in inequalities, we have to consider the values that makes the radicand non-negative and add this restriction to our solution set.