Simplify The Expression: ${-1 + (-3k) + (-8)}$
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Introduction
In algebra, simplifying expressions is a crucial skill that helps in solving equations and inequalities. It involves combining like terms and eliminating any unnecessary components. In this article, we will focus on simplifying the given expression: ${-1 + (-3k) + (-8)}$. This expression consists of three terms, and our goal is to simplify it by combining like terms.
Understanding the Expression
Before we start simplifying the expression, let's break it down and understand its components. The expression consists of three terms:
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{-1}$:$ This is a constant term, which means it does not contain any variable.
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{-3k}$:$ This term contains a variable, $k$, and a coefficient, $-3$. The coefficient is a numerical value that is multiplied by the variable.
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{-8}$:$ This is another constant term.
Combining Like Terms
Like terms are terms that have the same variable raised to the same power. In this expression, we have two constant terms and one term with a variable. To simplify the expression, we need to combine the constant terms and leave the term with the variable as it is.
Combining Constant Terms
The constant terms in the expression are ${-1}$ and ${-8}$. These terms can be combined by adding their coefficients.
{-1 + (-3k) + (-8) = -9 + (-3k)}$ ### Simplifying the Expression --------------------------- Now that we have combined the constant terms, we can simplify the expression further. The expression can be rewritten as: ${-9 - 3k}$ This is the simplified form of the given expression. ## Conclusion ---------- Simplifying expressions is an essential skill in algebra that helps in solving equations and inequalities. By combining like terms and eliminating unnecessary components, we can simplify complex expressions and make them easier to work with. In this article, we simplified the expression ${-1 + (-3k) + (-8)}$ by combining the constant terms and leaving the term with the variable as it is. The simplified form of the expression is ${-9 - 3k}$. ## Frequently Asked Questions --------------------------- ### Q: What is the simplified form of the expression ${-1 + (-3k) + (-8)}$? A: The simplified form of the expression is ${-9 - 3k}$. ### Q: How do I combine like terms in an expression? A: To combine like terms, you need to add or subtract the coefficients of the terms that have the same variable raised to the same power. ### Q: What is the difference between a constant term and a term with a variable? A: A constant term is a term that does not contain any variable, while a term with a variable is a term that contains a variable and a coefficient. ## Step-by-Step Solution ------------------------- ### Step 1: Identify the like terms in the expression. The like terms in the expression are the constant terms, ${-1}$ and ${-8}$. ### Step 2: Combine the like terms. The constant terms can be combined by adding their coefficients. ${-1 + (-8) = -9}$ ### Step 3: Simplify the expression. The expression can be simplified by rewriting it as: ${-9 - 3k}$ ## Example Problems ------------------- ### Problem 1: Simplify the expression ${2x + 3x + 4}$. ### Solution: The like terms in the expression are the terms with the variable, $x$. These terms can be combined by adding their coefficients. ${2x + 3x = 5x}$ The expression can be simplified as: ${5x + 4}$ ### Problem 2: Simplify the expression ${-2y + 3y - 5}$. ### Solution: The like terms in the expression are the terms with the variable, $y$. These terms can be combined by adding their coefficients. ${-2y + 3y = y}$ The expression can be simplified as: ${y - 5}$ ## Practice Problems ------------------- ### Problem 1: Simplify the expression ${4x + 2x - 3}$. ### Problem 2: Simplify the expression ${-5y + 2y + 1}$. ### Problem 3: Simplify the expression ${3x - 2x + 4}$. ### Problem 4: Simplify the expression ${-2y - 3y - 1}$. ### Problem 5: Simplify the expression ${2x + 4x - 2}$. ## Final Answer -------------- The final answer is ${-9 - 3k}$.<br/> # Simplify the Expression: A Comprehensive Guide to Algebraic Manipulation =========================================================== ## Q&A: Simplifying Expressions ----------------------------- ### Q: What is the purpose of simplifying expressions in algebra? A: The purpose of simplifying expressions in algebra is to make them easier to work with and to eliminate any unnecessary components. Simplifying expressions helps in solving equations and inequalities. ### Q: How do I identify like terms in an expression? A: Like terms are terms that have the same variable raised to the same power. To identify like terms, you need to look for terms that have the same variable and the same exponent. ### Q: What is the difference between combining like terms and simplifying an expression? A: Combining like terms involves adding or subtracting the coefficients of the terms that have the same variable raised to the same power. Simplifying an expression involves combining like terms and eliminating any unnecessary components. ### Q: Can I simplify an expression by combining unlike terms? A: No, you cannot simplify an expression by combining unlike terms. Unlike terms are terms that have different variables or different exponents, and they cannot be combined. ### Q: How do I simplify an expression with multiple variables? A: To simplify an expression with multiple variables, you need to identify the like terms and combine them. You can also use the distributive property to simplify the expression. ### Q: Can I simplify an expression with fractions? A: Yes, you can simplify an expression with fractions by combining the like terms and eliminating any unnecessary components. ### Q: How do I simplify an expression with negative coefficients? A: To simplify an expression with negative coefficients, you need to combine the like terms and eliminate any unnecessary components. You can also use the distributive property to simplify the expression. ### Q: Can I simplify an expression with parentheses? A: Yes, you can simplify an expression with parentheses by combining the like terms and eliminating any unnecessary components. ### Q: How do I simplify an expression with exponents? A: To simplify an expression with exponents, you need to combine the like terms and eliminate any unnecessary components. You can also use the power rule to simplify the expression. ### Q: Can I simplify an expression with radicals? A: Yes, you can simplify an expression with radicals by combining the like terms and eliminating any unnecessary components. ### Q: How do I simplify an expression with absolute values? A: To simplify an expression with absolute values, you need to combine the like terms and eliminate any unnecessary components. ### Q: Can I simplify an expression with inequalities? A: Yes, you can simplify an expression with inequalities by combining the like terms and eliminating any unnecessary components. ## Common Mistakes to Avoid --------------------------- ### Mistake 1: Combining unlike terms Combining unlike terms is a common mistake that can lead to incorrect solutions. Unlike terms are terms that have different variables or different exponents, and they cannot be combined. ### Mistake 2: Failing to simplify an expression Failing to simplify an expression can lead to incorrect solutions. Simplifying an expression involves combining like terms and eliminating any unnecessary components. ### Mistake 3: Using the wrong order of operations Using the wrong order of operations can lead to incorrect solutions. The order of operations is a set of rules that dictate the order in which mathematical operations should be performed. ### Mistake 4: Not checking for like terms Not checking for like terms can lead to incorrect solutions. Like terms are terms that have the same variable raised to the same power, and they can be combined. ## Tips and Tricks ------------------ ### Tip 1: Use the distributive property to simplify expressions The distributive property is a mathematical property that allows you to multiply a single term by multiple terms. Using the distributive property can help you simplify expressions and eliminate any unnecessary components. ### Tip 2: Use the commutative property to simplify expressions The commutative property is a mathematical property that allows you to rearrange the order of terms in an expression. Using the commutative property can help you simplify expressions and eliminate any unnecessary components. ### Tip 3: Use the associative property to simplify expressions The associative property is a mathematical property that allows you to rearrange the order of terms in an expression. Using the associative property can help you simplify expressions and eliminate any unnecessary components. ## Practice Problems ------------------- ### Problem 1: Simplify the expression ${2x + 3x + 4}$. ### Problem 2: Simplify the expression ${-2y + 3y - 5}$. ### Problem 3: Simplify the expression ${3x - 2x + 4}$. ### Problem 4: Simplify the expression ${-2y - 3y - 1}$. ### Problem 5: Simplify the expression ${2x + 4x - 2}$. ## Final Answer -------------- The final answer is ${-9 - 3k}$.</span></p>