Problem 9 Clear the fractions, and rewrite... [FREE SOLUTION]

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Elementary Algebra

Laura Bracken, Ed Miller

$Math Studyset 91影视 Explanations$ Math

1 Edition

Chapter 3: Problem 9

Clear the fractions, and rewrite each equation in standard form. $y-3=\frac{5}{8}(x+1)$

Short Answer

Expert verified

5x - 8y = -29

Step by step solution

Eliminate the fraction

To clear the fraction, multiply each term in the equation by 8, the denominator of the fraction: y - 3 = \frac{5}{8}(x + 1) \[8 \times (y - 3) = 8 \times \frac{5}{8}(x + 1)\] Simplify to get: \[8y - 24 = 5(x + 1)\]

Distribute and simplify

Distribute 5 on the right side of the equation: \[8y - 24 = 5x + 5\]

Rewrite in standard form

Rearrange the equation to be in standard form, which is Ax + By = C. Move all terms to one side and simplify: \[8y - 24 - 5x - 5 = 0\] Combine like terms: \[ -5x + 8y - 29 = 0\] Rearrange to standard form if needed: \[ 5x - 8y = -29\]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Standard Form Equations

Standard form equations in algebra are expressed as Ax + By = C, where A, B, and C are integers. This format is neat and consistent, making it easier to compare and analyze different equations. To get an equation into standard form, you often need to rearrange and simplify terms. For example, for the equation 5x + 8y = -29, A is 5, B is -8, and C is -29.
Notice how getting rid of fractions and distributing terms make it easier to reach the standard form.

Distributive Property

The distributive property allows you to multiply a value outside a set of parentheses by each term inside the parentheses. This helps in breaking down complex algebraic expressions. For instance, in the equation 8y - 24 = 5(x + 1), we apply the distributive property to 5(x + 1), resulting in 5x + 5.
Using this property simplifies expressions, making them easier to handle and solve.

Simplifying Algebraic Expressions

Simplifying algebraic expressions involves combining like terms and performing operations to make the expression easier to read and solve. In our exercise, 8y - 24 = 5x + 5, combine and simplify to remove any fractions or complex terms. Always check to ensure every term is simplified.
This step is crucial in getting your equation ready for further operations like rearranging or solving.

Rearranging Equations

Rearranging equations involves moving terms from one side of the equal sign to the other to achieve a desired form, like the standard form. In the equation -5x + 8y - 29 = 0, you can move all terms to one side to isolate variables or constants. This helps in solving for specific variables and provides a structured format for analysis.
Getting comfortable with rearranging terms is key to mastering algebraic manipulations.

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91影视

Clear the fractions, and rewrite each equation in standard form. \(y-3=\frac{5}{8}(x+1)\)

Short Answer

Step by step solution

Eliminate the fraction

Distribute and simplify

Rewrite in standard form

Key Concepts

Standard Form Equations

Distributive Property

Simplifying Algebraic Expressions

Rearranging Equations

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