Problem 64 Combine the like terms. $$9 p-... [FREE SOLUTION]

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Prealgebra

Julie Miller, Molly O鈥橬eill, Nancy Hyde

$Math Studyset 91影视 Explanations$ Math

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Chapter 3: Problem 64

Combine the like terms. $$9 p-13 p+p$$

Short Answer

Expert verified

-3p

Step by step solution

- Identify like terms

Look at the terms in the expression: $ 9p, -13p, \text{and} p $. All terms contain the variable $ p $, so they are like terms.

- Combine the coefficients

Add the coefficients of the like terms together: $ 9 - 13 + 1 $. Perform the calculations: $ 9 - 13 = -4 $ and then $ -4 + 1 = -3 $.

- Write the simplified expression

Combine the result with the variable: $ -3p $.

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Key Concepts

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

Coefficients

In algebra, coefficients are the numerical parts of the terms that include variables. Coefficients tell us how many times the variable is multiplied. For example, in the term $$9p$$, the coefficient is $$9$$, meaning $$p$$ is multiplied by $$9$$.
When you look at the original exercise, the terms are $$9p, -13p, \text{and} p$$. Here, $$9, -13,$$ and the implied $$1$$ (since $$p$$ is the same as $$1p$$) are coefficients.
Combating coefficients means adding or subtracting them as you would with ordinary numbers. So, if you combine $$9p - 13p + p$$ by adding the coefficients, you get $$9 - 13 + 1$$ resulting in the coefficient $$-3$$.

Variables

Variables are symbols used to represent numbers in algebraic expressions and equations. In our exercise, the variable is $$p$$. Variables are crucial as they allow a single expression or equation to represent multiple scenarios by taking different values.
In the given expression $$ 9p - 13p + p $$, the variable $$p$$ is consistent across all terms, making them like terms. This means they can be combined through their coefficients.
When terms have the same variable, combining them involves adding or subtracting their coefficients while keeping the variable intact. In our case, after simplifying, the term has a single variable $$p$$ with a coefficient.

Simplified Expressions

Simplified expressions are algebraic terms that have been reduced to their simplest form. This involves combining like terms and performing all possible arithmetic operations. Simplifying makes expressions easier to understand and work with.
In the exercise, we started with $$ 9p - 13p + p $$, which had multiple like terms. After combining the coefficients, we got $$ -3p $$ as the simplified expression.
Always look for like terms (those with the same variable) to combine. This process involves adding or subtracting their coefficients, as shown in the steps. Keeping expressions simplified helps in solving equations and further algebraic manipulations more efficiently.

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91影视

Combine the like terms. $$9 p-13 p+p$$

Short Answer

Step by step solution

- Identify like terms

- Combine the coefficients

- Write the simplified expression

Key Concepts

Coefficients

Variables

Simplified Expressions

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