Question

Solve each equation and check the result. $$r-(-7)=-1-6$$

   Solve each equation and check the result.
$$r-(-7)=-1-6$$

Prealgebra

Alan S. Tussy, R.… 4th Edition

Chapter 2, Problem 65

Instant Answer

Solved by Expert Casey Evans

07/19/2020

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This gives us: $$r + 7 = -1 - 6$$ Show more…

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Solve each equation and check the result. $$r-(-7)=-1-6$$

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Key Concepts

Linear Equations

Linear equations involve variables raised only to the first power. They are solved by isolating the variable on one side of the equation through a series of algebraic manipulations. This concept provides the foundation for solving many types of problems in algebra where the goal is to find the value of the unknown that makes the equation true.

Properties of Equality

The properties of equality state that an equal operation performed on both sides of an equation does not affect the equality. This concept is essential for performing operations such as addition, subtraction, multiplication, or division on both sides of an equation in a balanced and lawful manner, thereby maintaining the integrity of the equation.

Inverse Operations

Inverse operations are used to reverse the effects of operations to isolate the variable. For example, if a number is added to a variable, subtracting that same number helps to cancel it out. This concept is crucial for systematically undoing operations applied to a variable in order to solve an equation.

Arithmetic Operations with Negative Numbers

Arithmetic operations with negative numbers involve understanding how subtraction and addition work when negative signs are present. These operations are vital for correctly simplifying expressions and combining terms, especially when dealing with subtractions like subtracting a negative number, which is equivalent to addition.

Checking Solutions

Checking solutions involves substituting the found value of the variable back into the original equation to ensure that both sides agree numerically. This concept verifies the accuracy of the solution and helps confirm that no mistakes were made during the solving process.

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