Algebra - How To Solve Equations Quickly!

This segment introduces the topic of solving two-step equations, which encompass equations with fractions, parentheses, variables on both sides, and decimals. The presenter begins with the fundamental two-step equations, demonstrating how to isolate the variable 'x' by performing operations such as subtraction and division. An example equation, 3x + 5 = 17, is used to illustrate the process of isolating 'x' by first subtracting 5 from both sides and then dividing by 3 to solve for 'x'. The segment emphasizes the importance of performing opposite operations to isolate the variable and provides another example for the viewers to practice.

The second paragraph delves into more complex two-step equations, including those with variables on both sides of the equation. The presenter outlines strategies for dealing with equations that require moving all variable terms to one side and constants to the other, using examples such as 17 - 5x = 2 and 9 = 3 + x/4. The process involves subtracting constants and multiplying both sides by the reciprocal of the fraction to isolate the variable. The segment also covers checking solutions by substituting back into the original equation, ensuring the equation balances, which validates the solution.

This part of the script addresses multi-step equations that may involve combining like terms before performing the two-step process. The presenter guides through an example with multiple 'x' terms, 3x + 8 + 5x = 32, emphasizing the need to combine like terms first. The process involves subtracting constants and dividing by the coefficient of 'x' to solve for the variable. The segment reinforces the concept with another similar problem, highlighting the adaptability of the techniques to different forms of equations.

The fourth paragraph tackles equations where the variable 'x' appears on both sides, necessitating a strategic approach to isolate all 'x' terms on one side. Using an example like 13 - 2x = 4x, the presenter shows how to add 'x' terms to both sides and add constants to the other side to balance the equation. This method clears one side of the variable, allowing for straightforward division to solve for 'x'. The segment also encourages viewers to try a similar problem to practice this technique.

The final paragraph in the script introduces equations that include parentheses, requiring the use of the distributive property to simplify before solving. Examples like 3 * (2x - 4) + 1 = 7 are used to demonstrate how to distribute the multiplier across the terms inside the parentheses and then combine like terms. The presenter then guides through the process of adding or subtracting to isolate the variable, followed by division to find the value of 'x'. The segment also briefly mentions an algebra course available on Udemy, suggesting it as a resource for further learning.