Problem 14 - Elementary and Intermediate Algebra

Question

The Try Exercises for examples are indicated by a shaded block on the exercise number. Answers to these exercises appear at the end of the exercise set as well as at the back of the book. \(8 x,\) for \(x=7\)

Step-by-Step Solution

Answer

56

Step 1 - Understand the Variable

The expression given is 8x. Here, x is a variable which can take different values. In this specific problem, it is given that x equals 7.

Step 2 - Substitute the Value of x

Replace the variable x in the expression with the given value. Thus, the expression 8x becomes 8(7).

Step 3 - Perform the Multiplication

After the substitution, calculate the result of the multiplication. Multiply 8 by 7 to get the final value: 8 * 7 = 56.

Key Concepts

Substitution

Substitution in algebra involves replacing variables with their given values. For example, in the expression given in the original exercise (\(8x\)), the variable 'x' is set to 7. By substituting the value 7 for 'x', we change the expression from 8x to 8(7). Substitution helps to simplify algebraic expressions and is a key skill for solving equations.

• Identify the variable's value given in the problem.
• Replace the variable with this value in the mathematical expression or equation.

Once the substitution is done, you can proceed with other algebraic operations, like multiplication.

Variables in Algebra

Variables play a crucial role in algebra because they represent unknown values or quantities that can change. In the expression 8x, 'x' is the variable and its value can vary. Understanding variables is fundamental for forming and solving algebraic equations.

• Variables are often denoted by letters such as x, y, or z.
• They allow for general equations that can be solved for different values.

When we are given a specific value for the variable, we can substitute it as shown in the original exercise.

Multiplication in Algebra

Multiplication in algebra often involves variables and constants. In the context of the exercise, after substituting the value of x, we need to multiply 8 by 7. This operation follows the same rules as regular multiplication.

• Identify the numbers to be multiplied (constants and substituted variables).
• Perform the multiplication operation as usual.

In the original exercise, multiplying 8 by 7 gives us the result of 56. Remember that algebraic multiplication can also involve multiplying variables together, but in this case, it's about a constant and a variable's value.