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Chapter 9: Problem 40

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

Short Answer

Expert verified
The value of the expression \(4x+7\) when \(x=4\) is 23.

Step by step solution

01

Substitute the value of x

To find the value of the expression when \(x=4\), replace \(x\) with 4 in the expression \(4x+7\). So the expression becomes \(4(4) + 7\).
02

Perform the Multiplication

Calculate the value of \(4 \times 4\). This gives \(16\).
03

Add the Results

Now add the result of the multiplication to 7. So, \(16 + 7 = 23\).

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Key Concepts

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

Substitution Method
The substitution method is a handy tool for solving algebraic expressions, especially when you're given a specific value for a variable. Let's break down how this works using the expression given: \(4x + 7\) when \(x = 4\). This method involves replacing the variable with its specific value in the expression. In this case, you'll substitute \(x\) with \(4\).
  • Step 1: Identify the variable you need to replace. Here, it's \(x\).
  • Step 2: Substitute the number into the expression. So, replace \(x\) with \(4\) to get \(4(4) + 7\).
The beauty of the substitution method is its simplicity. You take something abstract (the variable \(x\)) and make it concrete by plugging in a real number. This technique helps clarify expressions and allows you to compute their value easily. Once you've substituted, the task becomes a matter of basic arithmetic.
Basic Arithmetic Operations
After substitution, the next step involves basic arithmetic operations. These operations are fundamental to mathematics and include addition, subtraction, multiplication, and division. Let's look at how they were applied here:
  • Multiplication: Once you substitute, the expression becomes \(4(4) + 7\). The first operation is multiplication. Calculate \(4 \times 4\), which equals \(16\).
  • Addition: The next operation is adding 7 to 16. This results in \(23\).
Each arithmetic operation should be performed step-by-step, respecting the order of operations (PEMDAS/BODMAS). Multiplication comes before addition according to these rules.
Practicing these basic operations boosts your confidence and skills in solving math problems. Remember that accuracy is key, so take your time to ensure each calculation is correct.
Prealgebra Problems
Prealgebra problems like the one solved here lay the groundwork for more complex algebraic concepts. They often involve evaluating expressions, understanding the order of operations, and substituting values into variables. These tasks are crucial for developing a deeper understanding of mathematics.
  • By tackling such problems, students build their skills in straightforward arithmetic, preparing them for algebraic challenges ahead.
  • Prealgebra serves as a bridge, transitioning from simple arithmetic to the structured language of algebra.
When solving prealgebra problems, attention to detail is crucial as it sets the stage for future learning. Mistakes made here can compound in more advanced math, so it鈥檚 essential to cement these basics. Consequently, practice and repetition are your best friends on this mathematical journey.

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Most popular questions from this chapter

Simplify the following expressions. \(\left(9 a^{5} b^{6}\right)^{2}\left(8 a^{5} b\right)\)

Expand and multiply. $$(2 x-4)^{2}$$

Multiply the following expressions. $$(x-2)(x+3)$$

Multiply the following expressions. $$(7 x-1)(4 x-5)$$

Write each expression with positive exponents, then simplify. $$3^{5} \cdot 3^{-8}$$
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