Solve the equations using the steps outlined in the text. 3(2 z-6)-4(3 z+1)=5-2(z+1)

Name: Problem 55, Chapter 9: Prealgebra & Introductory Algebra
Uploaded: 2022-04-03T13:54:54-08:00
Duration: 2 min 54 s
Channel: Erika Bustos
Description: Solve the equations using the steps outlined in the text. 3(2 z-6)-4(3 z+1)=5-2(z+1)

step 1 We need to solve the following. So we're going to get rid of our parentheses by using distribute

Solve the equations using the steps outlined in the text....

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Key Concepts

Distributive Property

The distributive property is a fundamental concept in algebra that allows you to multiply a single term by each term within a parenthesis, turning an expression like a(b + c) into ab + ac. This property is essential for expanding expressions and simplifying equations before combining like terms.

Combining Like Terms

Combining like terms involves simplifying an algebraic expression by adding or subtracting terms that have the same variable raised to the same power. This process reduces the complexity of the expression, making it easier to isolate the variable when solving an equation.

Solving Linear Equations

Solving linear equations involves finding the value of the variable that makes the equation true. This process typically includes applying the distributive property, combining like terms, and then isolating the variable through inverse operations, maintaining equality throughout the process.

Isolating the Variable

Isolating the variable means rearranging an equation so that all instances of the variable are on one side and all constant values are on the other side. This step is crucial for determining the exact value of the variable and includes operations such as addition, subtraction, multiplication, or division on both sides of the equation.

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