Problem 74
Question
Use the distributive property to rewrite each expression. $$ -11(x+4) $$
Step-by-Step Solution
Verified Answer
-11x - 44
1Step 1 - Distribute the Coefficient
Use the distributive property which states that for any numbers or expressions a, b, and c: a(b + c) = ab + ac Apply this to the given expression: -11(x + 4) = -11x + (-11)(4)
2Step 2 - Simplify the Expression
Multiply and simplify: -11x + (-11)(4) = -11x - 44.
Key Concepts
Algebraic ExpressionsCoefficientsSimplification
Algebraic Expressions
Algebraic expressions are mathematical phrases that can include numbers, variables, and operation symbols. For instance, in the exercise given, \(-11(x + 4)\) is an algebraic expression.
Here, \(x + 4\) is enclosed in parentheses, indicating that you should first distribute the \(-11\) across each term inside.
Algebraic expressions are very common in math and they help represent problems in a succinct and precise way. When dealing with algebraic expressions, always pay attention to variables, coefficients, and constants as these components play crucial roles.
This understanding will make solving and simplifying these expressions easier.
Here, \(x + 4\) is enclosed in parentheses, indicating that you should first distribute the \(-11\) across each term inside.
Algebraic expressions are very common in math and they help represent problems in a succinct and precise way. When dealing with algebraic expressions, always pay attention to variables, coefficients, and constants as these components play crucial roles.
This understanding will make solving and simplifying these expressions easier.
Coefficients
Coefficients are the numbers that are multiplied by the variables in algebraic expressions. In the expression from the exercise \(-11(x + 4)\), the number \(-11\) is the coefficient.
It tells us how many times to multiply the variable, which in this instance, is \(x\).
When you distribute \(-11\) across the terms inside the parentheses, you apply the distributive property which leads us to: \(-11 \cdot x + (-11) \cdot 4 \).
Understanding coefficients is key because they help us see the relationship between variables and constants within an equation.
Whenever you're simplifying expressions, keep an eye on the coefficients for accurate calculations.
It tells us how many times to multiply the variable, which in this instance, is \(x\).
When you distribute \(-11\) across the terms inside the parentheses, you apply the distributive property which leads us to: \(-11 \cdot x + (-11) \cdot 4 \).
Understanding coefficients is key because they help us see the relationship between variables and constants within an equation.
Whenever you're simplifying expressions, keep an eye on the coefficients for accurate calculations.
Simplification
Simplification is the process of making an algebraic expression easier to understand by combining like terms and performing basic arithmetic operations.
In the exercise, we simplify \(-11(x + 4)\) by first distributing the \(-11\) which results in \(-11x + (-11)(4)\).
Then, we perform the multiplication: \(-11 \cdot x = -11x \) and \(-11 \cdot 4 = -44 \). So, the simplified expression becomes \(-11x - 44\).
Simplification helps to reduce complex expressions into simpler forms, which makes them easier to work with in further calculations or solving equations.
Always take care to accurately perform multiplications, divisions, additions, and subtractions when simplifying to ensure correct results.
In the exercise, we simplify \(-11(x + 4)\) by first distributing the \(-11\) which results in \(-11x + (-11)(4)\).
Then, we perform the multiplication: \(-11 \cdot x = -11x \) and \(-11 \cdot 4 = -44 \). So, the simplified expression becomes \(-11x - 44\).
Simplification helps to reduce complex expressions into simpler forms, which makes them easier to work with in further calculations or solving equations.
Always take care to accurately perform multiplications, divisions, additions, and subtractions when simplifying to ensure correct results.
Other exercises in this chapter
Problem 73
Simplify each expression. \(3 t-5-2(2 t-4)\)
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Perform each indicated operation. \(|8-7(2)|-6(-2)\)
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Twelve divided by a number equals \(\frac{1}{3}\) times that number.
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Find each difference. $$ 5.7-(-11.6) $$
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