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Chapter 6: Problem 15

Add or subtract the monomials. $$28 x-(-12 x)$$

Short Answer

Expert verified
40x

Step by step solution

01

Identify the monomials

The monomials in the expression are \[ 28x \] and \[ -(-12x) \].
02

Simplify the negative sign

Simplify the expression by removing the parentheses. Since \[ -(-12x) \] is the same as \[ +12x \], the expression becomes: \[ 28x + 12x \].
03

Add the coefficients

Add the coefficients of \[ x \] together: \[ 28 + 12 = 40 \].
04

Write the final expression

Combine the coefficient with \[ x \]: \[ 40x \].

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Key Concepts

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

simplifying expressions
Simplifying expressions involves reducing them to their simplest form. In algebra, this often means combining like terms or eliminating unnecessary parentheses. Take the example \( 28 x-(-12 x) \).

In the first step, identify the monomials: \( 28x \) and \( -(-12x) \). Simplify the negative sign: \( -(-12x) \) is the same as \( +12x \). So, the expression becomes: \( 28x + 12x \).

This process helps make the expression easier to work with. By reducing the terms, we're also getting rid of any complexities that might make solving the problem harder. Remember, always break down the expression into smaller parts and look for terms that can be combined.
combining like terms
Combining like terms is a fundamental skill in algebra.
Like terms are terms that have the same variables raised to the same power, such as \( 28x \) and \( 12x \). To combine them, we add or subtract their coefficients.

In our problem, once simplified, the expression was \( 28x + 12x \). This means we look at the numbers in front of the variable \( x \), known as coefficients. Here, we have coefficients 28 and 12.

Add these coefficients together: \( 28 + 12 = 40 \). The variable remains the same, so the expression simplifies to \( 40x \).

Combining like terms makes the expression shorter and easier to understand. This allows for more efficient calculations in future steps.
coefficients
Coefficients are numbers in front of the variables.
In the term \( 28x \), the number 28 is the coefficient of \( x \). We use coefficients to perform operations such as addition and subtraction of terms.

In our exercise, we started with two terms: \( 28x \) and \( -(-12x) \). First, simplify \( -(-12x) \) to \( +12x \). Then add the coefficients 28 and 12 to get 40. This makes the final expression \( 40x \).

Understanding coefficients is essential not just for this exercise but for many other algebraic tasks. They help guide how we add and subtract terms, ensuring we correctly combine like terms and simplify expressions.

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Most popular questions from this chapter

Mixed Practice $$\frac{27 a^{7}}{3 a^{3}}+\frac{54 a^{9}}{9 a^{5}}$$

Divide each polynomial by the monomial. $$\left(9 n^{4}+6 n^{3}\right) \div 3 n$$

Divide the monomials. $$\frac{\left(6 a^{4} b^{3}\right)\left(4 a b^{5}\right)}{\left(12 a^{2} b\right)\left(a^{3} b\right)}$$

Divide each polynomial by the monomial. $$\frac{310 y^{4}-200 y^{3}}{5 y^{2}}$$

Divide each polynomial by the binomial. $$\left(m^{3}+1000\right) \div(m+10)$$
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