Problem 35 - Elementary and Intermediate Algebra

Question

Translate to an algebraic expression. 9 less than \(c\)

Step-by-Step Solution

Answer

\(c - 9\)

Step 1: Identify the keyword

The phrase 'less than' indicates subtraction.

Step 2: Determine the operation and order

In algebraic expressions, the term 'less than' suggests that we subtract a number from another number. In this case, we need to subtract 9 from the variable.

Step 3: Write the expression

Place the variable first, followed by the subtraction of 9. The expression becomes: \(c - 9\).

Key Concepts

subtraction in algebra

When we deal with algebraic expressions, subtraction is a common operation we use. The term 'less than' is a keyword that indicates subtraction. It tells us to take one number away from another.

In our exercise, '9 less than c' means we subtract 9 from the variable 'c'. In algebra, order matters. So, 'c - 9' is our correct expression. Always remember:

• The phrase 'less than' involves flipping the usual subtraction order.
• Whenever you see 'X less than Y', write it as 'Y - X'.

These rules help you avoid common mistakes and ensure you write the correct algebraic expressions.

variable manipulation

Variables in algebra represent unknown values. They can be manipulated using basic arithmetic operations like addition, subtraction, multiplication, and division.

In the given example, the variable 'c' stands for an unknown number. When we subtract 9 from 'c', we perform a variable manipulation:

• Variables can change positions in expressions based on the operation needed.
• Understanding how to manipulate variables is key to solving algebra problems.

So, instead of seeing 'c - 9' as just symbols, think of it as 'an unknown number minus 9'. This way, you grasp the concept better.

translating phrases to expressions

Translating phrases from words to algebraic expressions might seem tricky at first. But with practice, it gets easier.

First, identify the keywords in the phrase. For example, 'less than' suggests subtraction.

• Make sure you understand what each keyword means in algebraic terms.
• Know the order the operations should be performed.

In '9 less than c', we subtract 9 from the variable 'c', giving us 'c - 9'. Breaking down phrases like this helps you see the steps clearly and avoid errors. With practice, you'll become more confident in translating word problems into algebraic expressions.