In Exercises 1–16, evaluate each algebraic expression for the given value or values of the variable(s). x²-6x+3, for x=7

Verified step by step guidance

1. Substitute the given value of x (x = 7) into the algebraic expression x^2 - 6x + 3. This gives: $7^2-\; 6(7)\; +\; 3.$
2. Simplify the first term by calculating the square of 7: $7^2=\; 49.$
3. Simplify the second term by multiplying 6 by 7: $6(7)\; =\; 42.$
4. Combine the simplified terms into the expression: $49\; -\; 42\; +\; 3.$
5. Simplify the final expression by performing the subtraction and addition in order: $49\; -\; 42$ and then add 3.

Key Concepts

Algebraic Expressions

An algebraic expression is a mathematical phrase that can include numbers, variables, and operation symbols. In this case, the expression x^2 - 6x + 3 consists of a quadratic term (x^2), a linear term (-6x), and a constant term (3). Understanding how to manipulate and evaluate these expressions is fundamental in algebra.

Substitution

Substitution is the process of replacing a variable in an expression with a specific value. For the expression x^2 - 6x + 3, substituting x with 7 means replacing every instance of x in the expression with 7. This step is crucial for evaluating the expression and finding its numerical value.

Evaluating Expressions

Evaluating an expression involves performing the necessary arithmetic operations to simplify it to a single numerical value. After substituting the variable, you will calculate the result by following the order of operations (PEMDAS/BODMAS). This ensures that you correctly handle exponents, multiplication, and addition in the right sequence.