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Chapter 2: Problem 51

Find the terms of the expression. $$ -4-y $$

Short Answer

Expert verified
The terms of the expression '-4-y' are '-4' and '-y'.

Step by step solution

01

Identify the Terms

In the algebraic expression, the terms are the elements separated by '+' or '-'. In '-4-y', the operation 'subtract' is denoted by '-'. The terms are '4' and 'y' and both are separated by the subtraction operation '-'. One has to be careful because the sign '-' is associated with the term it precedes. As the term '4' and 'y' are preceded by '-', it is read as '-4' and '-y'.

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Key Concepts

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

Understanding Algebraic Expressions
Algebraic expressions are mathematical phrases that can include numbers, variables, and operations. An expression does not have an equal sign and thus differs from an equation. Instead, it is used to represent a value or set of values.

For example, in the expression \(-4 - y\), you see a mix of numbers and variables connected by the subtraction operation. Here's how you can break down any algebraic expression:
  • Numbers: Known as constants, these are the fixed values, like \(-4\).
  • Variables: Symbols, like \(y\), that can represent unknown values or values that can change.
  • Operations: Like addition or subtraction, these show how the numbers and variables interact.
Recognizing these elements is the starting point for working with algebra.
Subtraction in Algebra
Subtraction in algebra is about finding the difference between numbers, terms, or variables. In algebraic expressions, subtraction is indicated by a minus sign (-) and affects how the terms are expressed and collected.

In the expression \(-4 - y\), subtraction separates terms and also affects the values of those terms. The minus sign in front of a number or variable not only indicates subtraction but also implies that the term is negative:
  • \(-4\) means the number 4 is being subtracted or it is a negative value.
  • \(-y\) suggests that the variable \(y\) is being subtracted from something or it stands as a negative version of \(y\).
Understanding how subtraction works in expressions helps in simplifying and manipulating them according to algebraic rules.
Identifying Terms
Terms are the building blocks of algebraic expressions. Identifying them requires recognizing parts of the expression separated by plus (+) or minus (-) signs. A term can consist of a number, a variable, or a combination of both.

In the expression \(-4 - y\), the terms are:
  • \(-4\): This is a single term because it includes the negative sign and the number 4.
  • \(-y\): Here, the minus sign affects the variable \(y\), making it one complete term by itself.
It's essential to note that the negative sign is part of the term it directly precedes. Therefore, \(-4\) and \(-y\) are each single, separate terms. Recognizing this helps in analyzing and simplifying expressions accurately.

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Most popular questions from this chapter

EVALUATING EXPRESSIONS Evaluate the expression. $$ 4-8-3 $$

EXPRESSIONS WITH FRACTION BARS Evaluate the expression. $$ \frac{(2+5)^{2}}{3^{2}-2} $$

COMBINING LIKE TERMS Apply the distributive property. Then simplify by combining like terms. $$ 3 t(t-5)+6 t^{2} $$

Use the distributive property and mental math to simplify the expression. $$ -6 w-12-3 w+2 x^{2} $$

BUYING JEANS You have 58 dollar, and you want to buy a pair of jeans and a \(\$ 20\) T-shirt. There is a \(6 \%\) sales tax. If \(x\) represents the cost of the jeans, then the following inequality is a model that shows how much you can spend on the jeans. $$ x+20+0.06(x+20) \leq 58 $$ Simplify the left side of the inequality.
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