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Chapter 4: Problem 72

Identify the constant in the expression \(8 x-2\).

Short Answer

Expert verified
The constant in the expression \(8x - 2\) is \(-2\).

Step by step solution

01

Identify Terms in the Expression

The given expression is \(8x - 2\). It contains two terms: \(8x\) and \(-2\). Understanding the types of terms in the expression is the first step.
02

Determine Types of Terms

Next, identify the types of terms: \(8x\) is a variable term because it contains the variable \(x\), while \(-2\) is a constant term because it does not contain any variables.
03

Identify the Constant Term

Since \(-2\) is the term without any variables, it is identified as the constant in the expression.

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Key Concepts

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

Identifying Terms in Expressions
In algebra, an expression is a combination of different terms.
Terms are the individual parts of an expression, separated by plus or minus signs.
For example, in the expression \(8x - 2\), there are two terms: \(8x\) and \(-2\).
It is crucial to first identify these terms to understand and solve algebraic expressions correctly.
  • A term can be a number (constant), a variable, or a combination of both.
Let's move on to understanding the different types of terms.
Variable Terms
Variable terms are terms that include variables, such as letters representing unknown values.
In the expression \(8x - 2\), the term \(8x\) is a variable term because it includes the variable \(x\).
The coefficient of a variable term is the number multiplying the variable.
In \(8x\), the coefficient is 8.
  • Variables are usually represented by letters like \(x\), \(y\), or \(z\).
  • Coefficients give us more information about the term, such as how many times the variable is counted.
Variable terms change depending on the value of the variable.
Constant Terms
Constant terms are the terms in an expression that don鈥檛 change value since they do not contain any variables.
They are fixed numbers.
In the expression \(8x - 2\), the term \(-2\) is a constant term.
Constants are easy to identify because they are just numbers without any attached variables.
  • Constants provide a baseline value in the expression.
  • Unlike variable terms, constants remain the same regardless of any changes to the variables in the expression.
For the expression \(8x - 2\), the constant term is \(-2\).

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Most popular questions from this chapter

The cost of two jars of peanut butter and three jars of mayonnaise is $$\$ 10.87$$. The cost of five jars of peanut butter and four jars of mayonnaise is $$\$ 19.16$$. Find the cost of one jar of peanut butter. Find the cost of one jar of mayonnaise.

At a food co-op where co-op members are required to work 18 times per year, almonds cost \(\$ 9.46\) per pound and Brazil nuts cost \(\$ 7.31\) per pound. Find the amount of almonds and Brazil nuts needed to make \(40 \mathrm{lb}\) of a mixture that costs \(\$ 8\) per pound. Round to the nearest tenth.

Solve \(d=r t\) for \(r\).

For exercises 89-92, the completed problem has one mistake. (a) Describe the mistake in words, or copy down the whole problem and highlight or circle the mistake. (b) Do the problem correctly. Problem: Solve \(\begin{aligned} 2 x+3 y &=18 \\ x+2 y &=11 \end{aligned}\) by elimination. Incorrect Answer: $$ \begin{aligned} -2(2 x+3 y) &=-2(18) \quad 3(x+2 y)=3(11) \\ -4 x-6 y &=-36 \\ -4 x-6 y &=-36 \\ +3 x+6 y &=33 \\ \hline-x+0 &=3 \\ \frac{-x}{-1} &=\frac{3}{-1} \\ x &=-3 \\ x+2 y &=11 \\ -3+2 y &=11 \\ 2 y &=14 \\ \frac{2 y}{2} &=\frac{14}{2} \\ y &=7 \end{aligned} $$ The solution is \((-3,7)\).

Graph. Label the solution region.a $$ \begin{aligned} &y \leq x \\ &y \leq-x \\ &y \geq-8 \end{aligned} $$
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