Solve each equation. 7 x-6-5 x=-8

Name: Problem 64, Chapter 2: Intermediate Algebra for College Students
Uploaded: 2020-07-16T20:03:22-08:00
Duration: 1 min 27 s
Channel: Susan Cooper
Description: Solve each equation. 7 x-6-5 x=-8

Key Concepts

Inverse Operations

Inverse operations are used to reverse the effects of mathematical operations in order to isolate the variable. For instance, if a number is subtracted from the variable, adding the same number to both sides of the equation will cancel out the subtraction, and similarly, division can reverse multiplication. This concept is key to systematically solving equations.

Linear Equations

A linear equation is an equation in which the variable appears only to the first power and graphically represents a straight line. Understanding linear equations is fundamental in algebra, as they involve basic operations and provide a foundation for more complex mathematical problem-solving techniques.

Properties of Equality

The properties of equality are fundamental rules that allow for the same operations to be performed on both sides of an equation without changing its equality. These rules enable the step-by-step transformation of the equation while maintaining its balance, ensuring that the solution obtained is valid.

Isolating the Variable

Isolating the variable means manipulating the equation so that the unknown quantity is by itself on one side of the equality sign. This process involves using inverse operations and applying the properties of equality to systematically remove coefficients and constant terms from around the variable.

Simplifying Expressions

This concept involves combining like terms within an equation to make it simpler and more manageable. In a linear equation, terms that involve the variable are added together or subtracted from one another, while constant terms are also combined separately. This step is crucial for reducing the equation to its simplest form before taking further steps toward isolating the variable.

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