Problem 61 Translate to an equation and the... [FREE SOLUTION]

Chapter 2: Problem 61

Translate to an equation and then solve it. The sum of \(-4 n\) and \(5 n\) is \(-82 .\)

Short Answer

Expert verified

The value of n is -82.

Step by step solution

Translate the problem into an equation

Identify the mathematical expressions described in the problem. The sum of -4n and 5n is equal to -82. This can be written as the equation:ewlineewlinedash{-4n + 5n = -82}

Combine like terms

Combine the like terms on the left side of the equation, which simplifies to:ewlineewlinedash{(-4 + 5) n = -82}ewlineewlineSolving for the coefficients gives:ewlineewlinedash{1 n = -82}

Solve for n

Since 1n = n, the equation simplifies to:ewlineewlinedash{n = -82}

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Key Concepts

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

solving equations

Solving equations means finding the value of the variable that makes the equation true. In our problem, we need to find the value of \( n \) such that the sum of \( -4n \) and \( 5n \) equals \( -82 \). The steps to solve equations are straightforward:

Set up the equation based on the problem.
Simplify the equation if needed.
Isolate the variable.
Solve for the variable.

Let's use our problem to illustrate this process. Start with the equation: \(-4n + 5n = -82\). Simplify by combining like terms to get \( n = -82 \).

combining like terms

Combining like terms simplifies equations, making them easier to solve. Like terms have the same variable raised to the same power. In our problem, both terms \( -4n \) and \( 5n \) contain the variable \( n \).
To combine like terms, add or subtract their coefficients (the numbers in front of the variables). In this case, we combine \( -4n \) and \( 5n \) by calculating \( -4 + 5 \), which gives us \( 1 \). Hence, our equation becomes \( 1n = -82 \) or simply \( n = -82 \).
This simplified equation is much easier to work with and solve.

translating words to equations

Translating words to equations is about identifying the mathematical operations represented by words. Keywords like 'sum,' 'difference,' 'product,' and 'quotient' help you determine whether to add, subtract, multiply, or divide.
In our example, the phrase 'the sum of \( -4n \) and \( 5n \) is \( -82 \)' can be translated as:\[-4n + 5n = -82\].
This process involves:

Identifying keywords in the problem.
Determining the corresponding mathematical operations.
Writing the equation based on these operations.

Breaking down word problems into equations allows you to then apply algebraic techniques, making it simpler to find solutions.

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91影视

Translate to an equation and then solve it. The sum of \(-4 n\) and \(5 n\) is \(-82 .\)

Short Answer

Step by step solution

Translate the problem into an equation

Combine like terms

Solve for n

Key Concepts

solving equations

combining like terms

translating words to equations

One App. One Place for Learning.

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