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Solve for x. Enter the solutions from least to greatest. {:[(x-4)(-5x+1)=0],[" lesser "x=◻],[" greater "x=◻]:}

Solve for x x .\newlineEnter the solutions from least to greatest.\newline(x−4)(−5x+1)=0 lesser x=□ greater x=□ \begin{array}{l} (x-4)(-5 x+1)=0 \\ \text { lesser } x=\square \\ \text { greater } x=\square \end{array}

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Full solution

Q. Solve for x x .\newlineEnter the solutions from least to greatest.\newline(x−4)(−5x+1)=0 lesser x=□ greater x=□ \begin{array}{l} (x-4)(-5 x+1)=0 \\ \text { lesser } x=\square \\ \text { greater } x=\square \end{array}
  1. Factored Equation: Factored equation: (x−4)(−5x+1)=0(x-4)(-5x+1)=0\newlineTo find the roots, set each factor equal to zero and solve for xx.
  2. First Factor: First factor: x−4=0x - 4 = 0\newlineSolve for x:\newlinex−4+4=0+4x - 4 + 4 = 0 + 4\newlinex=4x = 4
  3. Second Factor: Second factor: −5x+1=0-5x + 1 = 0 Solve for xx: −5x+1−1=0−1-5x + 1 - 1 = 0 - 1 −5x=−1-5x = -1 x=−1/−5x = -1 / -5 x=1/5x = 1/5 or 0.20.2
  4. Final Solutions: Now we have two solutions for xx: 44 and 0.20.2. We need to enter the solutions from least to greatest. 0.20.2 is less than 44.

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