Problem 47 - Prealgebra

Question

Find the value of each of the following expressions when \(x = 5\). $$7 x-8$$

Step-by-Step Solution

Answer

The value of the expression is 27.

Step 1: Substitute the Variable

Substitute the given value of \(x\), which is 5, into the expression \(7x - 8\). This means replacing every occurrence of \(x\) with 5 in the expression.

Step 2: Perform Multiplication

After substitution, the expression becomes \(7(5) - 8\). Calculate the multiplication: \(7 \times 5 = 35\).

Step 3: Perform Subtraction

Now, substitute the result from the multiplication into the expression, which gives \(35 - 8\). Compute the subtraction: \(35 - 8 = 27\).

Key Concepts

Substitution in Algebraic Expressions

Substitution is a key concept in algebra that allows you to replace variables with specific values in an expression or equation. When solving problems that involve variables such as in the expression \(7x - 8\), substitution is often your first step.

• Identify the variable in the expression. In our case, this is \(x\).
• Replace this variable with the given value. Here, \(x = 5\).

After substitution, the expression \(7x - 8\) turns into \(7(5) - 8\). The variable \(x\) has been replaced by 5, making it possible to perform arithmetic operations. Substitution simplifies expressions, turning them into more manageable numerical problems that we can evaluate straightforwardly.

Understanding Multiplication of Expressions

Multiplication is an essential arithmetic operation used to evaluate expressions once substitution has been performed. After substituting \(x = 5\) into the expression \(7x - 8\), you redefine the equation as \(7(5) - 8\). This transformation highlights the importance of multiplication in algebra.

• Recognize that the coefficient (7) is multiplied by the substituted value (5).
• Carry out the multiplication: \(7 \times 5 = 35\).

This step simplifies the expression further, taking you one step closer to finding the final solution. Being able to multiply correctly is crucial for evaluating expressions accurately. Understanding multiplication helps you break down complex expressions into simpler parts.

Executing Subtraction in Expressions

Subtraction is the final operation you need to evaluate the expression \(7x - 8\) after performing substitution and multiplication. You now have a simplified part of the expression, \(35 - 8\), from the previous multiplication step. Here, subtraction comes into play to arrive at the final answer.

• Subtract the number 8 from the product 35.
• Compute the subtraction: \(35 - 8 = 27\).

After correctly performing the subtraction, you determine that the value of the original expression is 27 when \(x = 5\). Understanding how subtraction works in this context is vital, as it often represents the final step in evaluating many algebraic expressions. This operation helps you conclude the evaluation process efficiently and accurately.