Question

1. analyze problems if x represents the number of questions on a test, analyze the meaning of each expression: x + 4, x - 5, 2x, and x ÷ 3. 21. create write about a real - world situation that can be represented with an algebraic expression. then represent the situation with the expression.

Explanation:

For the first problem (question 19), we analyze each algebraic expression based on the context where \(x\) is the number of questions on a test. Addition (\(x + 4\)) implies more questions, subtraction (\(x-5\)) implies fewer questions, multiplication (\(2x\)) implies double the number of questions, and division (\(x\div3\)) implies dividing the number of questions into three - equal parts.
For the second problem (question 21), we need to think of a real - world scenario. For example, if we consider buying apples where the cost of one apple is \(a\) dollars and we buy \(n\) apples. The total cost \(C\) can be represented by the algebraic expression \(C = an\).

Answer:

19.

• \(x + 4\): The number of questions on the test increased by 4.
• \(x-5\): The number of questions on the test decreased by 5.
• \(2x\): The number of questions on the test is doubled.
• \(x\div3\): The number of questions on the test is divided into three equal - sized groups (or one - third of the number of questions on the test).

21.

• Real - world situation: Suppose you are buying pencils. Each pencil costs \(p\) dollars and you buy \(q\) pencils.
• Algebraic expression: The total cost \(T\) of buying the pencils is \(T = pq\).