CONCEPT PREVIEW Evaluate each expression. 3a - 2b, for a = -2 and b = -1

Verified step by step guidance

1. Identify the given expression and the values of the variables: the expression is \$3a - 2b\(, with \)a = -2\( and \)b = -1$.
2. Substitute the values of \(a\) and \(b\) into the expression: replace \(a\) with \(-2\) and \(b\) with \(-1\), so the expression becomes \$3(-2) - 2(-1)$.
3. Apply the multiplication operations: calculate \(3 \times (-2)\) and \(-2 \times (-1)\) separately.
4. Simplify the expression by performing the multiplications: this will give you two numbers to combine.
5. Combine the results by performing the subtraction operation to find the simplified value of the expression.

Key Concepts

Substitution in Algebraic Expressions

Substitution involves replacing variables in an expression with given numerical values. This is the first step in evaluating expressions, allowing you to simplify and calculate the result accurately.

Order of Operations

The order of operations dictates the sequence in which mathematical operations are performed: parentheses, exponents, multiplication and division (left to right), then addition and subtraction (left to right). Following this ensures correct evaluation of expressions.

Arithmetic with Negative Numbers

Understanding how to add, subtract, and multiply negative numbers is essential. For example, multiplying two negatives yields a positive, and subtracting a negative is equivalent to addition, which affects the final value of the expression.