Question

Match the solution given below on the number line to its inequality.

a. x > -9
b. x > -10
c. x > -8
d. x > -7

Answer 1

To match the solution given below on the number line to its inequality, we need to understand the concept of inequalities and number lines. An inequality is a mathematical statement that compares two expressions using symbols like >, <, ≥, ≤. A number line represents the real numbers graphically. The solution given below on the number line can be matched to its inequality using the symbols. a. x > -9 b. x > -10 c. x > -8 d. x > -7

Step-by-step explanation:

To match the solution given below on the number line to its inequality, we need to understand the concept of inequalities and number lines.

An inequality is a mathematical statement that compares two expressions using symbols like >, <, ≥, ≤. A number line represents the real numbers graphically.

a. x > -9: Represents all values greater than -9 on the number line.

b. x > -10: Represents all values greater than -10 on the number line.

c. x > -8: Represents all values greater than -8 on the number line.

d. x > -7: Represents all values greater than -7 on the number line.

Therefore, the matches are:

Solution Inequality

a x > -9

b x > -10

c x > -8

d x > -7

Answer 2

The matching of the solutions to their respective inequalities on the number line is as follows:

a. x > -9 corresponds to option c on the number line.

Step-by-step explanation:

In order to determine the correct match between the given solutions and their corresponding inequalities on the number line, we need to analyze each option.

Firstly, consider the inequality x > -9 (option a). This implies that x is greater than -9 but does not include -9 itself. Representing this on the number line, we would place an open circle at -9 and shade towards the right.

Similarly, for x > -10 (option b), we would place an open circle at -10 and shade towards the right, as it indicates values greater than -10 but not including -10.

Moving on to x > -8 (option c), we would place an open circle at -8 and shade towards the right. This signifies values greater than -8 but not including -8.

Lastly, for x > -7 (option d), an open circle would be placed at -7, and the shading would extend towards the right.

Comparing these representations to the given options, it becomes evident that option c (x > -8) is the correct match for x > -9. The open circle at -8 and shading towards the right aligns with the specified inequality, and therefore, option c is the correct solution on the number line.