Question

Paolo is solving the inequality 15+2x>31. To solve the inequality, he begins by solving the equation as shown. Which number line represents the solution to the inequality?

Answer 1

The answer is:

x > 8

Work/explanation:

To solve this inequality, I begin by subtracting 15 on each side:

`\sf{15+2x > 31}`

`\sf{2x > 31-15}`

`\sf{2x > 16}`

Divide each side by 2:

`\sf{x > 8}`

∴ x > 8

Answer 2

The graph in the attached figure

Explanation:

we have

`15+2x>31`

Subtract 15 both sides

`2x>31-15`

`2x>16`

Divide by 2 both sides

`x>16/2`

`x>8`

The solution is the interval (8,∞)

All real numbers greater than 8

In a number line is the shaded area at right of the number 8 (open circle)

see the attached figure to better understand the problem