Whether the given statement is true or false. If false, then to provide the correct statement. Given: The statement "The inequalities (x+3)(x−1)≥0 and x+3x−1≥0 have the same solution set."

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Whether the given statement is true or false. If false, then to provide the correct statement.  Given: The statement &quot;The inequalities (x+3)(x−1)≥0 and x+3x−1≥0 have the same solution set.&quot;

toroztatG · Accepted Answer

Consider the inequality (x+3)(x−1)≥0 and the function f(x)≥0.  It can be written as  f(x)=(x+3)(x−1)  It is clear that the function has x-intercept at -3, 1.  In the expression x+3x−1≥0, multiply both sides by (x−1)2:  x+3x−1≥0  x+3x−1×(x−1)2≥0×(x−1)2  (x+3)(x−1)≥0  Since both expressions are same, both have the same solution sets.  Conclusion: The provided inequalities have the same solution sets.

Whether the given statement is true or false. If false, then to provide the corr

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