Write The Following As An Inequality Calculator

How to Write Inequalities

Converting word problems to inequalities involves identifying key phrases that indicate relationships between quantities. Here's a step-by-step guide:

Step 1: Identify the Subject

Determine what the inequality is about. For example, if the problem is about the number of apples, the subject is "number of apples."

Step 2: Identify the Relationship

Look for words or phrases that indicate a relationship. Common phrases include "more than," "less than," "at least," and "at most."

Step 3: Identify the Comparison Value

Determine the value or quantity being compared to. For example, if the problem states "more than 5 apples," the comparison value is 5.

Step 4: Write the Inequality

Combine the subject, relationship, and comparison value into a mathematical inequality. For example, "The number of apples is more than 5" becomes "Number of apples > 5."

Common Inequality Types

Inequalities can be categorized based on the type of relationship they represent. Here are some common types:

1. Linear Inequalities

These involve a linear relationship between two variables. For example, "x is greater than 5" is written as x > 5.

2. Compound Inequalities

These involve multiple inequalities combined with "and" or "or." For example, "x is greater than 5 and less than 10" is written as 5 < x < 10.

3. Absolute Value Inequalities

These involve the absolute value of a variable. For example, "The distance from x to 5 is less than 2" is written as |x - 5| < 2.

4. Quadratic Inequalities

These involve quadratic expressions. For example, "x squared is less than 4" is written as x² < 4.

Solving Inequalities

Once you've written an inequality, you can solve it to find the range of values that satisfy the condition. Here's how to solve inequalities:

Step 1: Isolate the Variable

Perform operations to isolate the variable on one side of the inequality. For example, to solve 3x + 2 > 11, subtract 2 from both sides to get 3x > 9.

Step 2: Divide by the Coefficient

Divide both sides by the coefficient of the variable. For example, divide both sides of 3x > 9 by 3 to get x > 3.

Step 3: Consider the Inequality Direction

Remember that multiplying or dividing both sides of an inequality by a negative number reverses the inequality sign. For example, if you have -2x < 6, dividing by -2 gives x > -3.

Inequality Examples

Here are some examples of word problems converted to inequalities:

Example 1: Age Comparison

Problem: "John is older than Mark by at least 5 years."

Inequality: John's age ≥ Mark's age + 5

Example 2: Budget Constraint

Problem: "The total cost must be less than $100."

Inequality: Total cost < $100

Example 3: Temperature Range

Problem: "The temperature should be between 10°C and 20°C."

Inequality: 10°C ≤ Temperature ≤ 20°C

Example 4: Speed Limit

Problem: "The speed must not exceed 60 km/h."

Inequality: Speed ≤ 60 km/h