Challenge Problem Solve: (3)/(4) x-(1)/(5)((1)/(2)-3 x)+1=(1)/(4)((1)/(20) x+6)-(4)/(5)

Name: Problem 103, Chapter 1: Algebra and Trigonometry
Uploaded: 2021-06-13T11:48:58-08:00
Duration: 2 min 36 s
Channel: Yujie Wang
Description: Challenge Problem Solve: (3)/(4) x-(1)/(5)((1)/(2)-3 x)+1=(1)/(4)((1)/(20) x+6)-(4)/(5)

step 1 Let's solve this equation. So first, we just simplify this expression. Okay, distribute one fift

Challenge Problem Solve: (3)/(4) x-(1)/(5)((1)/(2)-3...

Key Concepts

Combining Like Terms

Combining like terms involves merging terms that have the same variables raised to the same power, thereby reducing the complexity of an expression. This step is key in simplifying both sides of an equation and is necessary for the effective isolation of variables.

Manipulating Fractions

Handling fractions correctly is crucial in algebra, particularly when equations include coefficients that are fractions. This involves operations such as finding common denominators, multiplying or dividing fractions, and simplifying complex fractional expressions to facilitate solving the equation.

Inverse Operations

Inverse operations are used to 'undo' operations applied to a variable, assisting in isolating the variable on one side of the equation. For instance, addition is undone by subtraction and multiplication by division. Mastering inverse operations is critical for solving linear equations and manipulating algebraic expressions.

Linear Equations

Linear equations are mathematical statements that equate two expressions involving a variable, usually arranged in the form ax + b = cx + d. Solving such equations involves isolating the variable on one side by performing equivalent operations on both sides of the equation. This foundational skill is essential for more advanced topics in algebra and beyond.

Distributive Property

The distributive property allows one to multiply a single term by each term within a parenthesis, transforming expressions such as a(b + c) into ab + ac. This property is fundamental when simplifying and expanding algebraic expressions, especially when fractions or negative signs are involved.

Transcript

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