91Ó°ÊÓ

Substitution is a fundamental concept in algebra that involves replacing a variable in an equation or expression with a given numerical value. This process allows us to evaluate expressions or solve equations. In our exercise, we replaced the variable \( x \) with its given value, which was 7. When substituting, it's essential to be accurate and meticulous to avoid any mistakes. By substituting \( x = 7 \) in the expression \( 15 - 2x \), the expression transforms into \( 15 - 2(7) \). This new expression no longer has variables and can be evaluated using numerical operations.

Order of operations is a set of rules that determines the sequence in which calculations should be performed to ensure accuracy. The rule often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)) helps avoid errors in solving expressions.

In the exercise, once we've substituted \( x = 7 \) to get \( 15 - 2(7) \), it's crucial to follow the correct order. First, we perform multiplication: \( 2 \times 7 = 14 \). After completing the multiplication, we move to subtraction, calculating \( 15 - 14 \) to reach the final result. Always ensure that each step is performed in the correct order to obtain a valid solution.

Integer arithmetic involves performing operations such as addition, subtraction, multiplication, and division on whole numbers, which can be positive, negative, or zero. Understanding how to manipulate these integers is essential for solving algebraic expressions.

In the given problem, we performed integer arithmetic by initially substituting and then operating with the integers: \( 15 - 2(7) \). The process included:

• Multiplication of integers \(2\) and \(7\), resulting in \(14\).
• Subtraction of \(14\) from \(15\), giving the final integer result of \(1\).

By practicing integer arithmetic, we enhance our ability to tackle more complex problems with confidence.