Algebra: Equations and Quadratic Equations
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Questions and Answers

What is the value of x in the equation 2x - 7 = 20?

  • 9
  • 6 (correct)
  • 5
  • 4
  • What is the value of p in the equation 8p + 14 = 5p + 17?

  • 3 (correct)
  • 5
  • 6
  • 7
  • What are the solutions to the quadratic equation x^2 = 144?

  • -12, 12 (correct)
  • -16, 16
  • -12, -12
  • 12, 12
  • What is the value of x in the inequality -3x < 27?

    <p>x &gt; -9</p> Signup and view all the answers

    Sarah bought 3 shirts and 2 pairs of pants for 85$. If each shirt costs 5$ more than each pair of pants, how much does each pair of pants cost?

    <p>20</p> Signup and view all the answers

    The length of a rectangle is 4 meters longer than its width. If the area of the rectangle is 60m^2, what is the width of the rectangle?

    <p>6</p> Signup and view all the answers

    Study Notes

    Equations

    • Equations are statements that express the equality of two mathematical expressions
    • Solving equations involves finding the value of the variable that makes the equation true

    Examples of Equations

    • 2у - 7 = 20
    • 4m - 16 = -36
    • 9 - x = x
    • 3t out of 4 = 18
    • (h - 7) out of 3 + 2 = 10
    • 13 + 6(f + 4) = 31
    • 8p + 14 = 5p + 17
    • 2 - 8a = 17 - 5a
    • 4(x - 2) = 3(x + 1)
    • 7w = 5(w - 2) + 16

    Quadratic Equations

    • Quadratic equations are equations of the form ax^2 + bx + c = 0, where a, b, and c are constants
    • Solving quadratic equations involves finding the roots or solutions of the equation

    Examples of Quadratic Equations

    • x^2 = 144
    • 3x^2 = 108
    • x^2 + 5 = 4
    • (x + 4)(x - 2) = 0
    • (3x - 2)(2x + 5) = 0
    • x^2 + 16x + 28 = 0
    • x^2 - 7x - 8 = 0
    • x^2 + 5x = 36

    Graphing Inequalities

    • Graphing inequalities involves representing the solution on a number line
    • The solution is represented by a shaded region or a point on the number line

    Examples of Graphing Inequalities

    • -3x < 27
    • x out of 6 ≥ 4

    Worded Quadratic Questions

    • Worded quadratic questions involve using algebra to solve real-world problems
    • These questions often involve translating words into algebraic equations

    Examples of Worded Quadratic Questions

    • Sarah bought 3 shirts and 2 pairs of pants for 85$. If each shirt costs 5$ more than each pair of pants, how much does each shirt and each pair of pants cost?
    • Alice is twice as old as Bob. In 6 years, the sum of their ages will be 54. How old are Alice and Bob now?
    • The length of a rectangle is 4 meters longer than its width. If the area of the rectangle is 60m^2, what are the dimensions of the rectangle?

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    Solve linear equations and quadratic equations, including word problems and different forms of quadratic equations. Practice solving for variables and finding all possible solutions.

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