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Chapter 1: Problem 42

Simplify each expression. $$ 19 x+x $$

Short Answer

Expert verified
20x

Step by step solution

01

Combine Like Terms

Identify the like terms in the expression. In this case, both terms are like terms because they both contain the variable 'x'. Therefore, combine the coefficients of 'x'.
02

Add the Coefficients

Add the coefficients of the like terms. In the expression, the terms are 19x and 1x. So, add the coefficients 19 and 1 to obtain the combined coefficient for 'x'.
03

Form the Simplified Expression

Write down the expression with the new coefficient. The new coefficient is 20, so the simplified expression is 20x.

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Key Concepts

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

Combining Like Terms
In algebra, combining like terms is an essential step to simplify expressions. Like terms are terms that contain the same variables raised to the same power.
It's important to remember that like terms can only be combined by performing operations on their coefficients.
For instance, in the expression 19x + x, both terms contain the same variable 'x', making them like terms.
Combining like terms helps reduce the expression to a more manageable form. By adding the coefficients of like terms, we condense multiple terms into a single term.
Coefficients
Coefficients are the numerical part of terms that contain variables.
They multiply the variables in an algebraic term and play a crucial role in combining like terms.
In the expression 19x + x, the coefficients are 19 and 1 respectively.
When combining like terms, we often add or subtract these coefficients. For example, adding the coefficients 19 and 1 gives 20, leading to the combined term 20x.
Understanding coefficients helps in efficiently simplifying algebraic expressions.
Simplified Expression
A simplified expression is an algebraic expression that has been reduced to its simplest form, where all possible like terms have been combined.
This process makes the expression clearer and easier to understand or further manipulate.
For example, starting with the expression 19x + x, we combine the coefficients (19 + 1) to get 20.
Therefore, the simplified expression is 20x, which is much clearer and straightforward.
Simplifying expressions is a fundamental skill in algebra, aiding in solving equations and understanding mathematical relationships.

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Most popular questions from this chapter

Simplify each expression. $$ -9 m^{3}+3 m^{3}-7 m^{3} $$

Translate each phrase into a mathematical expression. Use \(x\) as the variable. Combine like terms when possible. Six times a number added to \(-4,\) subtracted from twice the sum of three times the number and 4 (Hint: Twice means two times.)

Write a numerical expression for each phrase and simplify. The product of \(-9\) and \(2,\) added to 9

Write a numerical expression for each phrase and simplify. The sum of 15 and \(-3,\) divided by the product of 4 and \(-3\)

To find the average (mean) of numbers, we add the numbers and then divide the sum by the number of terms added. For example, to find the average of \(14,8,3,9,\) and \(1,\) we add them and then divide by 5. $$ \frac{14+8+3+9+1}{5}=\frac{35}{5}=7 \leftarrow \text { Average } $$ Find the average of each group of numbers. $$ -17,34,9,-2 $$
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