Question

Write each statement as an inequality. \(x\) is greater than or equal to 2

Short answer

The inequality is \( x \geq 2 \).

Step-by-step solution

Understand the given statement

The statement indicates that the variable \(x\) must be at least 2, meaning \(x\) can be 2 or any number greater than 2.

Choose the appropriate inequality symbol

Since \(x\) is greater than or equal to a specific value (2 in this case), the appropriate symbol to use is \( \geq \).

Write the inequality

Combine the variable \(x\) and the number 2 with the \( \geq \) symbol to form the inequality: \( x \geq 2 \).

Key concepts

greater than or equal to

The phrase 'greater than or equal to' means that a variable must be at least a certain value, but it can also be any number larger than that specific value.
For example, if we say, 'The number of apples in the basket is greater than or equal to 5,' this means there are at least 5 apples in the basket. There could be more than 5 apples, but not fewer.
This is symbolized using the \(\geq\) symbol in mathematics. So when we see an inequality like \(\alpha\geq 3\trash\), it means the variable \(\alpha\) is at least 3 or more.

inequality symbols

In mathematics, inequality symbols are used to compare values and express the relationship between them.
These symbols are:

• **\(>\)** for 'greater than', e.g.,\( x > 2 \)
• **\(<\)** for 'less than', e.g., \( y < 5 \)
• **\(\geq\)** for 'greater than or equal to', e.g., \( x \geq 2 \)
• **\(\leq\)** for 'less than or equal to', e.g., \( z \leq 10 \)

Inequalities allow us to define ranges or constraints for variables. These are crucial in problem-solving and mathematical modeling because they help set boundaries and conditions. For example, in the statement \( x \geq 2 \), the inequality tells us that the smallest value \( x \) can take is 2, but it could be larger.

variable constraints

Variable constraints are conditions or limits placed on variables.
They help specify the range of values that a variable can take. For example, in \( x \geq 2 \), the constraint means that \( x \) cannot be less than 2. Variable constraints often occur in the form of inequalities because they define the permissible values in different contexts.
Understanding constraints is important across various areas of mathematics and science.
Key Points to Remember:

• Constraints limit the possible values of a variable
• They often appear in equations and inequalities
• They help identify valid solutions to problems

For instance, when solving a problem, identifying and understanding these constraints ensures that the solution is feasible and adheres to given conditions.