For exercise, solve the equations and inequalities. Write the solutions sets to the inequalities in interval notation if possible. 1x2−14x+40≤0

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For exercise, solve the equations and inequalities. Write the solutions sets to the inequalities in interval notation if possible.  1x2−14x+40≤0

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Step 1: Analysis Given: 1x2−14x+40≤0 To determine the solution sets of the given inequality. Step 2: Simplification Factorising the term x2−14x+40. Let p(x)=x2−14x+40 p(x)=x2−14x+40 =x2−4x−10x+40 =x(x−4)−10(x−4) =(x−10)(x−4) when x=10,4.p(x)=0 when x∈(−∞,4).p(x)&amp;gt;0 when x∈(4,10).p(x)&amp;lt;0 when x∈(10,∞).p(x)&amp;gt;0 Step 3: Solution For 1x2−14x+40≤0. x2−14x+40 should be less than 0. x2−14x+40&amp;lt;0 when x∈(4,10) Therefore, the solution set of the given inequality is (4,10)

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

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