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Solve for x. Enter the solutions from least to greatest. {:[x^(2)-4x+3=0],[" lesser "x=◻],[" greater "x=◻]:}

Solve for x x . Enter the solutions from least to greatest.\newlinex2−4x+3=0 lesser x=□ greater x=□ \begin{array}{l} x^{2}-4 x+3=0 \\ \text { lesser } x=\square \\ \text { greater } x=\square \end{array}

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Q. Solve for x x . Enter the solutions from least to greatest.\newlinex2−4x+3=0 lesser x=□ greater x=□ \begin{array}{l} x^{2}-4 x+3=0 \\ \text { lesser } x=\square \\ \text { greater } x=\square \end{array}
  1. Identify Quadratic Equation: Identify the quadratic equation to be solved.\newlineThe given quadratic equation is x2−4x+3=0x^2 - 4x + 3 = 0. We need to find two numbers that multiply to give the constant term (3)(3) and add up to give the coefficient of the xx term (−4)(-4).
  2. Factor the Equation: Factor the quadratic equation.\newlineThe two numbers that multiply to 33 and add up to −4-4 are −1-1 and −3-3. Therefore, we can factor the quadratic equation as follows:\newlinex2−4x+3=(x−1)(x−3)=0x^2 - 4x + 3 = (x - 1)(x - 3) = 0
  3. Solve for x: Solve for x by setting each factor equal to zero.\newlineFirst, set the first factor equal to zero:\newlinex−1=0x - 1 = 0\newlineAdd 11 to both sides to solve for x:\newlinex=1x = 1\newlineNext, set the second factor equal to zero:\newlinex−3=0x - 3 = 0\newlineAdd 33 to both sides to solve for x:\newlinex=3x = 3
  4. Write Solutions in Ascending Order: Write the solutions in ascending order.\newlineThe solutions are x=1x = 1 and x=3x = 3. Since 11 is less than 33, the solutions in ascending order are 1,31, 3.

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