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Chapter 1: Problem 92

In the following exercises, translate from algebra to English. $$6n = 36$$

Short Answer

Expert verified
Six times a number is equal to thirty-six.

Step by step solution

01

Identify the Components

The equation has two components: the variable term (6n) and the constant term (36).
02

Translate the Variable Term

The variable term 6n means 'six times a number (n)'.
03

Translate the Equality

The equality sign = translates to 'is equal to'.
04

Translate the Constant Term

The constant term 36 remains 'thirty-six'.
05

Combine the Translations

Combine the translations from the previous steps: 'Six times a number is equal to thirty-six'.

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Key Concepts

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

Translating Algebraic Expressions
When faced with an algebraic expression, step one is to understand each part of it. These expressions typically include variable terms and constants.

For example, in the expression 6n, '6' is a constant, and 'n' is the variable. The constant multiplies the variable, so we interpret 6n as 'six times a number'. Imagine the variable 'n' as any number you could choose.

Translating algebraic expressions into plain English can make solving them easier. By turning 6n into 'six times a number', you make the math problem more understandable.

Always remember to identify constants (numbers) and variables (letters). This process helps you convert algebraic expressions into words.
Algebraic Equations
An algebraic equation is a statement that two expressions are equal. It includes an equality sign '='. This symbol tells us that the values on both sides of it are the same.

For instance, in the equation 6n = 36, the equality sign shows that 'six times a number' is equal to 'thirty-six'. Without the '=' sign, it would just be an expression, not an equation.

Equations allow us to find unknown numbers, represented by variables. To solve equations, you follow a series of steps to isolate the variable and find its value.

Having a clear understanding of how to translate these components is crucial for solving algebra problems effectively.
Variable Terms
A variable term contains a number (coefficient) and a letter (variable). The coefficient tells you how many times to multiply the variable.

In 6n, '6' is the coefficient, and 'n' is the variable. We read this as 'six times a number'. The variable 'n' can represent any unknown number.

Understanding variable terms helps you break down algebraic equations into simpler parts. Once you can identify and translate them, solving the equation becomes manageable.

To summarize, variable terms are the heart of many algebra problems. Recognizing them in equations is the first step to mastering algebra.

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Most popular questions from this chapter

Convert the units. At take-off, an airplane weighs 220,000 pounds. Convert the weight to tons.

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Convert the units. An empty bus weighs 35,000 pounds. Convert the weight to tons.

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