Algebra: Equations and Quadratic Equations

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?