Solve the equation (1)/(2)(x-7)=(3)/(4)(2 x+1).

Name: Problem 107, Chapter 4: Intermediate Algebra for College Students
Uploaded: 2020-07-24T00:56:18-08:00
Duration: 1 min 40 s
Channel: Ankit Gupta
Description: Solve the equation (1)/(2)(x-7)=(3)/(4)(2 x+1).

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Key Concepts

Distributive Property

The distributive property is a fundamental algebraic rule which states that multiplying a sum by a number equals the sum of the individual products of each addend with that number. It is used to expand expressions and simplify equations by removing parentheses.

Combining Like Terms

Combining like terms is the process of simplifying algebraic expressions by merging terms that have the same variable parts. This helps in reducing the complexity of an equation, facilitating the isolation of the variable to solve for its value.

Linear Equations

Linear equations are expressions involving variables raised only to the first power and constants. The goal in solving them is to isolate the unknown variable by performing a sequence of algebraic operations that preserve equality, ultimately finding the unique solution that satisfies the equation.

Clearing Fractions

Clearing fractions is a technique used when solving equations that contain fractions. By multiplying both sides of an equation by a common denominator, fractions are eliminated, making the equation simpler and easier to manipulate with standard algebraic methods.

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