Problem 9 Simplify each expression. \(7 ... [FREE SOLUTION]

Chapter 1: Problem 9

Simplify each expression. \(7 t+18-4\)

Short Answer

Expert verified

7t + 14

Step by step solution

- Identify and Combine Like Terms

In the expression, identify like terms that can be combined. Here, the terms are: the constant terms 18 and -4, and the variable term 7t.

- Combine the Constant Terms

Add the constant terms: 18 + (-4) = 14.

- Write the Simplified Expression

Combine the result from Step 2 with the variable term 7t to get the final simplified expression: 7t + 14.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Combining Like Terms

Combining like terms is a fundamental concept in algebra that involves simplifying expressions by merging terms with identical variables.
For an expression like the one given in the exercise (7t + 18 - 4), you first need to identify which terms can be combined.
In this case, like terms include the constant terms and the variable term.
Let鈥檚 break this down:

LIKE TERMS: Terms that have the same variables raised to the same powers, such as 7t, 3t, and -2t.
THE CONSTANT TERMS: Numbers without variables are always considered like terms together.

By combining like terms, you reduce the expression to its simplest form. This is done by adding or subtracting the coefficients of the like terms.

Constant Term

A constant term is a term in an algebraic expression that does not contain any variables.
In our exercise, the terms 18 and -4 are constant terms.
To simplify these, combine them as you would with regular numbers.
Here鈥檚 how this works:

First, note the constants: 18 and -4.
Next, combine the constants: 18 + (-4) = 14.

Constant terms are straightforward as they do not involve any variables, making them easy to add or subtract directly.

Variable Term

A variable term includes variables and their coefficients. For example, in the expression 7t + 18 - 4, the variable term is 7t.
The coefficient here is 7, and the variable is t.
Here鈥檚 a breakdown of variable terms:

IDENTIFYING VARIABLES: These are symbols that represent unknown values, like t, x, or y.
COEFFICIENT: The number multiplying the variable (e.g., 7 in 7t).

When simplifying an expression, variable terms are kept as they are if they have no like terms to combine with.
In our problem, the final simplified expression retains the variable term as 7t.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Simplify each expression. \(7 t+18-4\)

Short Answer

Step by step solution

- Identify and Combine Like Terms

- Combine the Constant Terms

- Write the Simplified Expression

Key Concepts

Combining Like Terms

Constant Term

Variable Term

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Probability and Statistics

Logic and Functions

Geometry

Theoretical and Mathematical Physics

Pure Maths

Study anywhere. Anytime. Across all devices.