Ch. P - Fundamental Concepts of Algebra

Blitzer8th EditionCollege AlgebraISBN: 9780136970514Not the one you use?Change textbook

Blitzer 8th Edition

Ch. P - Fundamental Concepts of Algebra

Problem 1

Chapter 1, Problem 1

In Exercises 1–16, evaluate each algebraic expression for the given value or values of the variable(s). 7+5x, for x = 10

Verified step by step guidance

Step 1: Start with the given algebraic expression: 7 + 5x.

Step 2: Substitute the given value of x (x = 10) into the expression. This means replacing 'x' with '10' in the expression.

Step 3: Rewrite the expression after substitution: 7 + 5(10).

Step 4: Simplify the multiplication first, as per the order of operations (PEMDAS/BODMAS). Multiply 5 by 10.

Step 5: Add the result of the multiplication to 7 to complete the evaluation of the expression.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Algebraic Expressions

An algebraic expression is a mathematical phrase that can include numbers, variables, and operation symbols. It represents a value that can change depending on the values assigned to its variables. For example, in the expression 7 + 5x, '7' is a constant, '5' is a coefficient, and 'x' is a variable.

Substitution

Substitution is the process of replacing a variable in an expression with a specific value. This is a fundamental technique in algebra that allows us to evaluate expressions. In the given expression 7 + 5x, substituting x with 10 means replacing 'x' with '10' to compute the value of the expression.

Evaluating Expressions

Evaluating an expression involves performing the operations indicated in the expression after substituting the variables with their respective values. This process results in a numerical value. For instance, evaluating 7 + 5(10) requires calculating the multiplication first, followed by the addition, leading to the final result.

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