I. Introduction
Inequality is a common mathematical concept that deals with the idea of comparing the values of two expressions using a symbol, such as >, <, ≥, or ≤. In this article, we will focus on the inequality x 4 2 and explore which number line represents the solutions to this equation. The purpose of this article is to help readers understand how to interpret and graph number lines for this type of inequality.
II. Understanding Inequalities: Interpreting Number Lines for x > 4 and x < 2
Before we delve into solving this particular inequality, let’s first understand what an inequality is and how it differs from an equation. An equation is a statement indicating that two expressions are equal, while an inequality indicates that one expression is greater than or less than another expression.
To interpret number lines for x > 4 and x < 2, we need to start by plotting the points 4 and 2 on the number line. Then, we draw an arrow or line that extends in either direction from each point, depending on whether x is greater than or less than the value of the point. For x > 4, we draw an arrow pointing to the right from the point 4, and for x < 2, we draw an arrow pointing to the left from the point 2.
Visual aids help to illustrate these concepts even better. In Fig. 1 and Fig. 2 below, we show how these number lines would look on a real y-axis.
Figure 1: Number line for x > 4
III. Solving Inequalities: Examining the Correct Number Line for x 4 2
To solve the inequality x 4 2, we need to isolate x by subtracting 2 from both sides of the equation:
x + 2 – 2 > 4 – 2
x > 2
Now, we know that x is greater than 2, so we need to determine whether the solution is x > 4 or x < 2 based on the mathematical reasoning behind the inequality. Since the expression is x 4 2, we can imagine the inequality as an inequality of distances on a number line, where x is certain distance away from 2.
Since the inequality expresses that x is more than or equal to two units away from 2, the solution can only be represented as x > 4. This is illustrated in Fig. 3 below:
Figure 3: Number line representing the solution x > 4
