Looking for a Tutor Near You?

Post Learning Requirement »
x

Choose Country Code

x

Direction

x

Ask a Question

x

x
Hire a Tutor
DISCOVER

Algebra

Loading...

Published in: Mathematics
10 Views

Simplifying expressions solving equations and working with inequalities

Basit A / Doha

2 years of teaching experience

Qualification: Masters

Teaches: Mental Maths, Olympiad Exam Preparation, English, Economics, Statistics, Accountancy: Management, Accountancy: Tax, Bookkeeping, Finance: Banking, Finance: Corporate, Finance: Planning, Business Training, Asset Management, Cost Accounting, Quickbooks Training

Contact this Tutor
  1. Algebra: Simplifying Expressions, Solving Equations, and Working with Inequalities Welcome to the world of algebra! This presentation provides a comprehensive overview of essential algebraic concepts, ranging from simplifying expressions to solving complex equations and inequalities. By the end of this presentation, pu'll gain a solid understanding of how to manipulate algebraic expressions, solve linear and quadratic equations, and work with inequalities. Whether you're a student looking to improve your algebra skills or simply someone interested in exploring the beauty of mathematics, this presentation is designed to equip you with the knowledge and confidence you need to succeed. 0) by Bigga Faith Made With Gamma
  2. Introduction to Algebra What is Algebra? Algebra is a branch of mathematics that uses symbols and letters to represent numbers and quantities. It's a powerful tool for solving problems and making generalizations about mathematical relationships. Algebra builds upon arithmetic, introducing variables and algebraic expressions. Key Concepts Variables are symbols (usually letters) that represent unknown quantities. Constants are fixed values that don't change. Expressions are combinations of variables, constants, and operations e, -t x, Equations are statements that two expressions are equal. Why Study Algebra? Algebra provides a foundation for higher-level mathematics, such as calculus and linear algebra. It's essential for solving problems in science, engineering, economics, and computer science. Algebra also develops critical thinking and problem- solving skills applicable to everyday life. Made With Gamma
  3. Simplifying Algebraic Expressions 1 Combining Like Terms Like terms are terms that have the same variables raised to the same powers. To combine like terms, add or subtract their coefficients. For example, 3x 5x = 8x and 7y - 2y = 5y. Remember, pu can only combine like terms! 2 Distributive Property The distributive property states that •c) = ac. This property is used to multiply a term by an expression inside parentheses. For instance, 2(x * 3) = 2x 4 6. Apply carefully, especially with negative signs. 3 Order of Operations (PEMDAS) The order of operations (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) is crucial for simplifying expressions correctly. Always perform operations in the correct order to avoid errors. For example, 5 2 x 3 = 5-6=11. Made With Gamma
  4. Properties of Exponents and Radicals Exponent Rules When multiplying exponents with the same base, add the exponents: x" m • = When dividing, subtract the exponents: / = Power to a power: (x'm)'n = These are foundational rules for manipu lating exponential expressions. Simplifying Radicals A radical is simplified when the radicand (the number under the radical) has no perfect square factors. For example, $12 = C (4 • 3) = Rationalizing the denominator is also a key technique. Fractional Exponents Fractional exponents represent radicals. For example, x'(1/2) = C x and x '(min) = nth root of (x' m). Understanding this relationship allows you to convert between exponential and radical forms. Made With Gamma
  5. Solving Linear Equations 1 2 Isolate the Variable The goal is to isolate the variable on one side of the equation. Use inverse operations to undo operations performed on the variable. For instance, if the equation is x 5 = 10, subtract 5 from both sides. Addition and Subtraction Add or subtract the same value from both sides of the equation to maintain equality. If you have x - 3 = 7, add 3 to both sides toget x = 10. This is a fundamental principle in solving equations. 3 Multiplication and Division Multiply or divide both sides of the equation by the same non-zero value. If 2x = 8, divide both sides by 2 to get x = 4. Avoid multiplying or dividing by zero, as it leads to undefined results. Made With Gamma
  6. Solving Quadratic Equations Factoring Factor the quadratic expression into two binomials. Set each binomial equal to zero and solve for x. For example, • 5x + 6 = 2)(x +3) = O, sox = -2 or x = -3. Factoring is most effective for simpler quadratics. Quadratic Formula The quadratic formula, x = (-b ± C (b"2 - 4ac)) / (2a), can solve any quadratic equation in the form ax"2 bx • c = O. It's a versatile method that always yields the solutions, even when factoring is difficult Completing the Square Rewrite the quadratic equation in the form (x 4 h)n2 = k. Take the square root of both sides and solve for x. This method is useful for understanding the structure of quadratic equations and deriving the quadratic formula. Made With Gamma
  7. Graphing Linear Equations Slope-Intercept Form Write the equation in the form y = mx b, where m is the slope and b is the pintercept. The slope indicates the steepness and direction of the line, while the y-intercept is where the line crosses the y-axis. 2 3 Plotting Points Choose tvw or more x-values, substitute them into the equation, and find the corresponding y-values. Plot these points on a coordinate plane and draw a line through them. More points provide more accuracy. Using Intercepts Find the x-intercept by setting y = O and solving for x. Find the y-intercept by setting x = O and solving fory. Plot these intercepts on a coordinate plane and draw a line through them. This can be a quick method when intercepts are easily found. Made With Gamma
  8. Solving Systems of Linear Equations Substitution Method Solve one equation for one variable and substitute that expression into the other equation. Solve for the remaining variable. Substitute the value back into one of the original equations to find the value of the other variable. Graphical Method Graph both equations on the same coordinate plane. The point of intersection is the solution to the system. If the lines are parallel, there is no solution. If the lines are the same, there are infinitely many solutions. 1 2 3 Elimination Method Multiply one or both equations by constants so that the coefficients of one variable are opposites. Add the equations together to eliminate that variable. Solve for the remaining variable. Substitute the value back into one of the original equations to find the value of the other variable. Made With Gamma
  9. Inequalities and Their Graphs 2 3 Solving Inequalities Solve inequalities similarly to equations, but remember to flip the inequality sign when multiplying or dividing by a negative number. This is a critical difference that must be remembered. Graphing Inequalities Use a number line to represent the solutions. Use an open circle for e: or > and a closed circle for or Shade the region that represents the solutions. use the graph to visualize the range of values that satisfy the inequality. Compound Inequalities Solve and graph each inequality separately, then find the intersection (AND) or union (OR) of the solutions. The intersection represents values that satisfy both inequalities, while the union represents values that satisfy either inequality. Made With Gamma
  10. Applications of Algebra in the Real World Construction Algebra is used to calculate measurements, angles, and material quantities in construction projects. Accurate algebraic calculations ensure structural integrity and efficient use of resources. Finance Algebra is used to calculate interest rates, loan payments, and investment returns. Understanding algebraic concepts is crucial for making informed financial decisions. Science Algebra is used to model and solve problems in physics, chemistry, and biology. Scientific experiments often rely on algebraic equations to analyze data and draw conclusions. Made With Gamma

Need a Tutor or Coaching Class?

Post an enquiry and get instant responses from qualified and experienced tutors.

Post Requirement

Related Study Notes

Upload Study Notes

If you have your own Study Notes which you think can benefit others, please upload on MyPrivateTutor. For each approved Study Note you will get 100 Credit Points and 100 Activity Score which will increase your profile visibility.

Upload Now
Home > Study Notes > Algebra