Problem 44 Find the value of each of the fo... [FREE SOLUTION]

91影视

Prealgebra

Charles P. McKeague

$Math Studyset 91影视 Explanations$ Math

6 Edition

Chapter 9: Problem 44

Find the value of each of the following expressions when $x=-3$. $$4 x+7$$

Short Answer

Expert verified

The expression evaluates to $-5$ when $x=-3$.

Step by step solution

Substitute the Value of x

First, we need to substitute the given value of $x$ into the expression. The expression given is $4x + 7$, and we are asked to evaluate it when $x = -3$. So, substitute $-3$ for $x$ in the expression, which becomes $4(-3) + 7$.

Calculate the Multiplication

Now, calculate the multiplication operation. Multiply 4 by $-3$, resulting in $-12$. So, the expression becomes $-12 + 7$.

Perform the Addition

Finally, perform the addition operation. Add $-12$ and 7, which gives $-5$. So, the value of the expression when $x=-3$ is $-5$.

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Key Concepts

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

Evaluating Expressions

Evaluating an expression involves finding its value by substituting variables with specific numbers. In the given exercise, you are asked to evaluate the expression $4x + 7$ when $x = -3$. This process can often be broken down into a few straightforward steps:

Start by substituting the value of the variable into the expression.
Next, follow the order of operations (often remembered by PEMDAS/BODMAS) to simplify the expression. This often involves performing multiplication or division before addition or subtraction.

In our example, we substitute $-3$ for $x$, and then simplify the expression step by step, leading to the result of $-5$. Making sure to work through each calculation carefully ensures that you get the correct result.

Integer Arithmetic

Integer arithmetic involves conducting mathematical operations with whole numbers, including positive numbers, negative numbers, and zero. This type of arithmetic is foundational in prealgebra and is crucial when evaluating algebraic expressions.

Multiplication and Division: When multiplying or dividing integers, the sign of the result depends on the signs of the numbers involved. For instance:
- Multiplying two positive or two negative numbers gives a positive result.
- Multiplying a positive number by a negative number yields a negative result.
Addition and Subtraction: When adding or subtracting integers, consider the signs again. Adding a negative number is the same as subtracting its positive counterpart.

In our expression, multiplying $4$ with $-3$ results in $-12$. Following that, adding $-12$ and $7$ gives the result of $-5$. Careful attention to the signs helps avoid common mistakes.

Prealgebra

Prealgebra is an essential mathematical stepping stone. It prepares you for more advanced algebra by focusing on core concepts like variables and arithmetic operations. Understanding prealgebra involves:

Grasping basic arithmetic operations including addition, subtraction, multiplication, and division.
Familiarity with working with variables, where letters like 'x' can represent numbers.
Learning how to evaluate expressions by substituting variables with given numbers.

In your exercise, using prealgebra concepts enabled the evaluation of $4x + 7$ by understanding how to substitute $x$ with $-3$. This type of practice is crucial for gaining confidence and skill in solving algebraic equations. Mastering prealgebra provides a solid foundation for tackling more complex mathematical problems in the future.

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91影视

Find the value of each of the following expressions when \(x=-3\). $$4 x+7$$

Short Answer

Step by step solution

Substitute the Value of x

Calculate the Multiplication

Perform the Addition

Key Concepts

Evaluating Expressions

Integer Arithmetic

Prealgebra

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