Problem 7 - Algebra and Trigonometry

Question

Evaluate each algebraic expression for the given value or values of the variable(s). $$x^{2}-6 x+3, \text { for } x=7$$

Step-by-Step Solution

Answer

The evaluated value of the algebraic expression given \(x=7\) is 10.

Step 1: Substitute the Value

In our algebraic expression \(x^2 - 6x + 3\), we are given that \(x = 7\). So, we simply replace each all value of x in the expression with 7, getting \(7^2 - 6(7) + 3\).

Step 2: Simplify using Order of Operations

Now we perform the operations following the order of operations (PEMDAS/BODMAS): First the exponent, then the multiplication and finally the addition. The exponentiation gives \(7^2 = 49\), the multiplication gives \(6(7) = 42\), so our expression becomes \(49 - 42 + 3\). Subtraction and addition give \(-42 + 49 + 3 = 10\).