Question

What is the geometric meaning of \(-5<-2\) ? A. -2 is not as negative as -5 . B. -5 is to the left of -2 on the number line. C. -5 is smaller than -2 . D. -2 is to the right of -5 on the number line.

Short answer

B and D

Step-by-step solution

Understand the inequality

The given inequality is \(-5 < -2\). This means that -5 is less than -2.

Analyze the number line

On the number line, smaller numbers are to the left and larger numbers are to the right.

Place numbers on the number line

Position -5 and -2 on the number line: \(..., -5, ..., -2, ...\). Here, -5 is to the left of -2.

Interpret the geometric meaning

Given that -5 is to the left of -2, we select the option that confirms this spatial relationship.

Select the correct answer

Option B: \(-5 \text{ is to the left of } -2 \text{ on the number line}\) and Option D: \(-2 \text{ is to the right of } -5 \text{ on the number line}\) are equivalent and correct.

Key concepts

inequality comparison

Inequality comparison is a crucial concept in mathematics. It helps us understand the relative size of different numbers. When we see an inequality like \(-5 < -2\), it simply means that -5 is less than -2. To put it into perspective, think about comparing two quantities. In this case, \(-5\) represents a value that is smaller than \(-2\). Hence, inequalities give us a way to compare numbers and understand their relative positions.

number line placement

A number line is a visual way to see how numbers are arranged. When placing numbers on a number line, smaller numbers appear to the left while larger numbers appear to the right. For example, if we plot -5 and -2, you'll see that -5 is positioned to the left of -2. This visual perspective can make understanding inequalities easier. Draw a simple number line and practice placing different numbers on it. This will help grasp the idea that being to the 'left' means being smaller, and being to the 'right' means being larger.

geometric interpretation of inequalities

Geometric interpretation of inequalities involves understanding these concepts visually. Take the inequality \(-5 < -2\) as an example. On a number line, \(-5\) is to the left of \(-2\). This visual representation shows the spatial relationship between the two numbers. Not only does \(-5\) come before \(-2\) on the number line, but it also indicates that -5 is a smaller value compared to -2. Geometric interpretation helps solidify your understanding of inequalities by linking abstract concepts with visual cues. Visualizing numbers this way can make solving inequalities more intuitive.