Question

Which inequality is represented by the following number line?

0 1 2 3 4 5 6 7 8 9 10
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1
A. 3x+6≤10
B. 31x+61≤12
C. 3x−6≥15
D. 31⋅(−6)=18

Answer 1

Without the specific number line, we can't determine the exact inequality it represents. However, solving each given inequality helps us understand how to represent them on a number line. For instance, 3x+6≤10 would have a solution set of x-values less than or equal to ⅗, whereas 3x−6≥15 would have x-values greater than or equal to 7.

Step-by-step explanation:

To determine which inequality is represented by a number line, we have to solve each inequality and see which one fits the values indicated on the number line. Since no specific number line with values was provided, I'll give a general approach to solving inequalities.

For example, for the inequality 3x+6≤10, we would solve for x:

• Subtract 6 from both sides: 3x ≤ 4
• Divide both sides by 3: x ≤ ⅗

This means the solution set includes all x-values less than or equal to ⅗, which you can represent on a number line with a closed circle at ⅗ and a shaded line extending to the left.

In contrast, for inequality 3x−6≥15, solving for x would look like this:

• Add 6 to both sides: 3x ≥ 21
• Divide both sides by 3: x ≥ 7

This inequality would show on a number line with a closed circle at 7 and a shaded line extending to the right, representing that x can be any value greater than or equal to 7.