Problem 4 - Beginning and Intermediate Algebra

Question

7 less than a number \(x\) is represented by A. \(7-x\) B. \(7

Step-by-Step Solution

Answer

D. \(x - 7\)

Step 1 - Understand the Expression

Identify the phrase '7 less than a number.' This means you need to subtract 7 from some number.

Step 2 - Translate into an Equation

The phrase 'a number' is represented by the variable \(x\). Therefore, '7 less than a number' is mathematically represented as \(x - 7\), since you are subtracting 7 from \(x\).

Step 3 - Match with Given Options

Compare our expression \(x - 7\) with the given options. We find that Option D matches: \(x - 7\).

Key Concepts

Understanding Variables

In algebra, variables are symbols used to represent unknown quantities. Typically, we use letters like x, y, and z. When you see a variable, think of it as a placeholder for a number you don't know yet. For example, in the expression 'a number less 7,' the variable x stands in for 'a number.' This simple approach helps make complicated problems easier to solve because it allows you to set up and manipulate equations.

Here are a few key points to remember about variables:

• They are usually represented by letters.
• They hold the place for unknown numbers.
• They are crucial in forming equations that you can solve.

By understanding variables, you'll have a solid foundation for solving a range of algebraic problems.

Translating Phrases to Equations

Translating phrases into mathematical equations is an essential skill in algebra. It allows you to understand and solve word problems systematically. Let's break down the process using our example '7 less than a number'.

Here’s the step-by-step approach:

• Identify the variable: In our case, 'a number' is represented by the variable x.
• Understand the operation: The phrase '7 less than' means you need to subtract 7 from the number.
• Form the equation: Putting it all together, '7 less than a number' translates to the equation x - 7.

Translating phrases to equations involves similar steps regardless of the problem. First, pinpoint the variable. Next, identify mathematical operations suggested by the words. Then, construct the equation that reflects the problem statement. With practice, you’ll find this becomes almost second nature!

Solving Word Problems

Word problems can often seem tricky, but breaking them into manageable steps makes them much more approachable. Here’s how you can go about solving word problems effectively:

• Read the problem carefully: Understand what is being asked. Identify the key terms and quantities involved.
• Identify the variable: Decide which quantity is unknown and choose a variable to represent it.
• Translate the words into an equation: Use your understanding of the problem to form the appropriate equation.
• Solve the equation: With the equation in place, you can now solve for the unknown variable.
• Check your work: Verify your solution by plugging the number back into the original problem to see if it makes sense.

Let’s revisit our example: '7 less than a number x.' Following the steps, we identified x as the variable and translated the phrase into x - 7. Comparing it with the provided options, we saw that the correct match was x - 7, which is Option D. By applying these steps consistently, solving word problems becomes a structured and less intimidating task.