Problem 90 - Algebra A Combined Function

Question

Write each sentence as an equation or inequality. Use \(x\) to represent any unknown number. The difference of sixteen and four is greater than ten.

Step-by-Step Solution

Answer

The inequality is \(16 - 4 > 10\).

Step 1: Understand the sentence structure

The sentence given is 'The difference of sixteen and four is greater than ten.' Breaking it down, 'difference' means subtraction, so you will be subtracting one number from another. Here, the numbers are 16 and 4.

Step 2: Translate the subtraction part into an expression

The phrase 'the difference of sixteen and four' translates to the mathematical expression \(16 - 4\).

Step 3: Understand the inequality part

The phrase 'is greater than ten' means you are comparing the expression from step 2 to the number 10 using a greater-than inequality.

Step 4: Formulate the inequality

Combine the expression \(16 - 4\) with the inequality symbol '>'. Thus, the entire sentence 'The difference of sixteen and four is greater than ten.' becomes the inequality \(16 - 4 > 10\).

Key Concepts

Inequality Formulation

When working with algebraic inequalities, the first step is understanding how to convert a verbal sentence into a mathematical inequality. This requires breaking down the sentence into smaller parts and identifying key elements like operations and comparisons. The sentence 'The difference of sixteen and four is greater than ten' is a perfect example.

To begin, identify the operation, which in this case is 'difference,' indicating subtraction. Next, recognize what you're comparing, which here is that the result of the subtraction is 'greater than' ten. Putting it all together involves taking these parts and forming them into a single mathematical statement.

Learning how to formulate inequalities from sentences is essential because it allows us to translate real-world situations into mathematical form, making them easier to solve and understand.

Sentence to Mathematical Expression

Translating a sentence into a mathematical expression involves careful reading and understanding. Consider the phrase 'the difference of sixteen and four.'

• 'Difference' suggests a subtraction operation.
• Numbers given are sixteen (16) and four (4) which leads to the expression: \(16 - 4\).

Upon identifying subtraction, the next step is ensuring that this expression faithfully represents the phrase. In many exercises, you might face terms like 'sum,' 'product,' or 'quotient,' indicating addition, multiplication, and division, respectively. Developing a keen sense of these terms will enhance your ability to interpret word problems quickly and correctly.

Moreover, practicing transforming sentences into expressions helps in visualizing mathematical concepts, making it easier to solve complex problems.

Greater Than Inequality

The phrase 'is greater than' describes a comparison that leads to an inequality. Recognizing 'greater than' in a sentence is crucial because it signals the use of the '>' symbol in mathematics.

• It tells us that one quantity exceeds the other.
• In our example, the phrase 'is greater than ten' shows that the result of \(16 - 4\) exceeds 10.

Once the ">" symbol is identified, you can easily convert the words into an inequality: \(16 - 4 > 10\). This inequality now directly expresses the initial statement mathematically.

Understanding greater than inequalities is essential in math as they are widely used to describe relationships and make decisions based on numerical data. Mastering these concepts opens the door to solving a variety of problems effectively.