Question

Write each statement as an inequality. \(x\) is less than 2

Short answer

x < 2

Step-by-step solution

- Identify the variable and quantity

The variable given is \(x\) and the quantity it is compared to is 2.

- Determine the inequality type

Since the problem states that \(x\) is less than 2, we need to use a less than inequality symbol.

- Write the inequality

Combine the variable and the quantity with the correct inequality symbol to form the inequality: \(x < 2\).

Key concepts

writing inequalities

Writing inequalities is an important concept in algebra.
It involves expressing the relationship between two expressions where one expression is not equal to the other.
This concept is used in many real-life situations, like comparing heights, weights, or prices.
In our example, we have the statement '\text{\(x\) is less than 2}' to convert into an inequality.
First, identify the variable, which is \(x\).
Next, determine the quantity it is compared to, which in this case, is 2.
Finally, since \(x\) is less than 2, we use the less than symbol with \(x\) and 2.
This gives us the inequality: \(x < 2\).
This method of writing inequalities is simple and can be applied to many similar problems.
Just remember to correctly identify your variable and quantity, and choose the right inequality symbol.

less than symbol

The less than symbol (<) is used to show that one value is smaller than another.
In our inequality \(x < 2\), the less than symbol tells us that \(x\) is on the left and is smaller than 2, which is on the right.
This is an essential part of writing algebraic inequalities and understanding their meaning.
It's important to remember the direction of the less than symbol:

• The pointed end faces the smaller quantity
• The open end faces the larger quantity

This helps visually compare the two quantities.
Understanding this symbol is crucial for solving and graphing inequalities.
When graphing \(x < 2\) on a number line, we would draw an open circle at 2 and shade all the numbers to the left.
This visually shows all possible values of \(x\) that are less than 2.

problem-solving steps

Solving algebraic inequalities involves a few simple but important steps.
The exercise we solved can be broken down into these steps:

Step 1: Identify the variable and quantity: Determine the variable (\(x\)) and the number (\(2\)) from the given statement.

Step 2: Determine the inequality type: Understand whether it is a less than, greater than, less than or equal to, or greater than or equal to statement.
In this case, it's a less than inequality.

Step 3: Write the inequality: Combine the variable and the number using the appropriate inequality symbol.
So, for '\(x\) is less than 2', we write \(x < 2\).
Each step builds on the previous one, so following them in order is crucial.
Use these steps whenever you're faced with a problem involving inequalities to make the process much simpler and clearer.