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Questions and Answers
What is the value of x in the equation 2x - 7 = 20?
What is the value of x in the equation 2x - 7 = 20?
What is the value of p in the equation 8p + 14 = 5p + 17?
What is the value of p in the equation 8p + 14 = 5p + 17?
What are the solutions to the quadratic equation x^2 = 144?
What are the solutions to the quadratic equation x^2 = 144?
What is the value of x in the inequality -3x < 27?
What is the value of x in the inequality -3x < 27?
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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?
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?
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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?
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?
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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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Description
Solve linear equations and quadratic equations, including word problems and different forms of quadratic equations. Practice solving for variables and finding all possible solutions.
