Problem 13 - Algebra 1

Question

Write the verbal phrase as an algebraic expression. Use \(x\) for the variable in your expression. Nine more than a number.

Step-by-Step Solution

Answer

The algebraic expression for the verbal phrase 'Nine more than a number' is 'x + 9'.

Step 1: Understand the Verbal Phrase

In the verbal phrase 'Nine more than a number', the words 'more than' suggest the operation of addition, while 'a number' implies a variable. Since the variable to be used is specified as 'x', 'a number' is symbolized by 'x'.

Step 2: Translate 'Nine More Than'

'Nine more than' translates to the operation of adding nine to something. In algebraic expressions, this is represented as '+9'.

Step 3: Formulate the Total Expression

Combine the variable and the operation from the previous steps, to create the complete algebraic expression. In this case, since 'nine more than a number' implies adding 9 to a certain variable 'x', it's written as 'x + 9'.

Key Concepts

Verbal Phrases

Verbal phrases are ways to express mathematical ideas using words instead of symbols. They are important because they allow us to translate our daily language into mathematical language. Understanding verbal phrases lets us convert spoken or written questions into algebraic expressions that can be solved.

In mathematics, you often encounter phrases such as:

• 'more than', indicating addition
• 'less than', suggesting subtraction
• 'times', hinting at multiplication
• 'divided by', denoting division

Each of these verbal cues helps pinpoint which mathematical operation is needed.

Let's apply this knowledge to our example: The phrase 'Nine more than a number' tells us to think about addition. 'More than' indicates that we are talking about adding something, which in this instance, is nine.

Addition in Algebra

Addition in algebra involves bringing together numbers and variables to form an algebraic expression or equation. Recognizing the operation of addition through verbal cues is essential for forming correct expressions.

When you hear 'more than' or see similar phrases, these are hints to use the addition operation. In the context of an algebraic expression, addition is straightforward:

• The symbol for addition is '+'.
• It doesn't matter which number you assign first or second; the expression is still equivalent. For example, 'Nine more than a number' translates to the expression 'number plus nine', or algebraically, 'x + 9'.
• Addition is commutative, meaning the order doesn't affect the outcome: 'x + 9' is the same as '9 + x'.

By recognizing these elements, you can confidently translate and solve addition problems in algebra.

Variables in Algebra

Variables are symbols used to represent numbers whose exact values are not yet known. They are fundamental to creating algebraic expressions and are often given reserve letters like 'x', 'y', or 'z'.

In an algebraic context, variables allow us to generalize mathematical sentences. Instead of having a fixed number, a variable can take on different values.

• For example, in the verbal phrase 'a number', the specific number isn't defined, so we use a variable, here referred to as 'x'.
• Variables allow expressions to be flexible, and they enable us to solve for unknown values once additional information is provided.
• In the expression 'x + 9', 'x' is the variable, and '9' is a constant, thus forming a simple yet powerful algebraic expression.

By understanding variables, you can write expressions and equations that stand for numerous possible numerical scenarios.