ROOT FUNCTIONS Solving Radical Inequalities (Page 1 of 2)

Solving a radical inequality is nearly the same as solving an equation. In fact, we solve the equation first using the x-intercept method, then analyze the graph to determine the solution set of the inequality.

To solve the inequality sqrt(2x-5)-2 < sqrt(x-2), first get a zero on the right: sqrt(2x-5)-2-sqrt(x-2) < 0. Then replace the inequality symbol with an equal sign: sqrt(2x-5)-2-sqrt(x-2) = 0. This equation was solved in the previous example using CALC zero and the solution was determined to be x = 27. The graph of the function represented by the left side of the equation, f(x) = sqrt(2x-5)-2-sqrt(x-2), is shown along with the zero.

GRAPH key. Calculator screen image.
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