Algebra - How To Solve Equations Quickly!

This paragraph introduces the topic of solving two-step equations, covering basics such as equations with fractions, parentheses, variables on both sides, and decimals. The speaker begins by demonstrating how to solve a simple equation, 3x + 5 = 17, through the process of isolating the variable x. The explanation includes subtracting 5 from both sides to eliminate the constant term and then dividing by 3 to find the value of x, which is 4. The paragraph continues with similar examples, such as 4x + 3 = 19 and 17 - 5x = 2, illustrating the steps of subtraction and division to solve for x. The examples aim to teach viewers how to manipulate equations to isolate the variable and find the solution.

This paragraph delves into more complex two-step equations where variables are present on both sides of the equation. The speaker provides a step-by-step guide on how to approach these problems, emphasizing the importance of moving all variable terms to one side and constants to the other. Examples given include equations like 9 = 3 + x/4 and 8 + x/3 = 12, where the speaker demonstrates subtracting constants and multiplying both sides to eliminate fractions and isolate the variable. The paragraph also covers scenarios with multiple x terms, such as 3x + 8 + 5x = 32, and shows how to combine like terms before solving. The goal is to simplify the equation into a form that can be easily solved by standard algebraic methods.

The focus of this paragraph is on solving equations that include parentheses, which often require the use of the distributive property. The speaker explains how to distribute a term across parentheses and then combine like terms to simplify the equation. Examples such as 3 * (2x - 4) + 1 = 7 and 5 * (3x + 4) = 37 + 2 are used to illustrate the process. The speaker shows how to multiply through the parentheses, combine constants, and then isolate the variable term to solve for x. This paragraph helps viewers understand how to handle more complex algebraic expressions involving parentheses and demonstrates the systematic approach to solving such equations.

This paragraph addresses the challenge of solving equations that contain multiple fractions or decimals. The speaker introduces strategies for dealing with fractions, such as finding a common multiple to eliminate them, as shown in the example with two fractions. For decimals, the approach involves multiplying through by a power of 10 to clear the decimal points. The speaker provides examples with step-by-step solutions, such as multiplying every term by 6 to clear fractions in one equation and by 10 to eliminate decimals in another. The goal is to simplify the equations to a form where standard algebraic methods can be applied to find the value of x.

In the final paragraph, the speaker transitions from solving equations to promoting an algebra course available on Udemy. The course is described as covering a wide range of topics from basic arithmetic to more advanced algebraic concepts. The speaker outlines the course content, which includes sections on fractions, linear equations, order of operations, graphing linear equations, inequalities, polynomials, factoring, systems of equations, quadratic equations, rational and radical expressions, complex and imaginary numbers, exponential and logarithmic functions, conic sections, and sequences and series. Each section is said to include video quizzes for review. The speaker invites viewers to explore the course and provides a direct link to it on Udemy, aiming to support those who wish to deepen their understanding of algebra.