Solve each equation. -4(2 z-6)=-3(z-4)+z

Name: Problem 86, Chapter 2: Intermediate Algebra for College Students
Uploaded: 2020-05-16T19:26:29-08:00
Duration: 48 s
Channel: Jake Zanazzi
Description: Solve each equation. -4(2 z-6)=-3(z-4)+z

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Key Concepts

Distributive Property

The distributive property allows you to multiply a factor by each term within a parenthesis. In solving equations, it is used to eliminate parentheses and simplify expressions, which is crucial when the equation contains expressions like -4(2z - 6) or -3(z - 4). This property is a fundamental tool in algebra that helps to correctly expand and simplify terms before combining like terms.

Combining Like Terms

Combining like terms involves adding or subtracting coefficients of the same variable to simplify an expression. This is important in solving equations because it reduces the equation to a simpler form, making it easier to isolate the variable. It ensures that all similar terms are consolidated, thereby facilitating the process of balancing the equation.

Solving Linear Equations in One Variable

Solving linear equations in one variable involves isolating the variable to find its value. This process typically includes applying the distributive property, combining like terms, and using inverse operations. The goal is to perform equivalent operations on both sides of the equation so that the variable stands alone on one side, which is a central strategy in algebraic problem-solving.

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