For exercise, solve the equations and inequalities. Write the solutions sets to the inequalities in interval notation if possible. −5x(x−3)22+x≤0

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For exercise, solve the equations and inequalities. Write the solutions sets to the inequalities in interval notation if possible.  −5x(x−3)22+x≤0

SabadisO · Accepted Answer

Step 1 To solve the following inequality: −5x(x−3)22+x≤0 Step 2 Calculation: Since, −5x(x−3)22+x≤0 Multiplying both sides by -1, we get 5x(x−3)22+x≥0 Dividing both sides by 5, we get, x(x−3)22+x≥0 The critical points are x=0,x=−2,x=3 Step 3 Sign of x(x−3)22+x can be summarized in the following table. Range of xSign of x(x−3)22+xx&amp;lt;−2positivex=−2not defined−2&amp;lt;x&amp;lt;0negativex=0zero0&amp;lt;x&amp;lt;3positivex=3zerox&amp;gt;3positive Hence, x(x−3)22+x≥0 is satisfied when x&amp;lt;−2,x=0,0&amp;lt;x&amp;lt;3,x&amp;gt;3 Therefore, given inequality is satisfied is x&amp;lt;−2 and x≥0 Hence, given inequality is satisfied if x∈(−2,0]∪[0,∞)

For exercise, solve the equations and inequalities. Write the solutions sets to

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