Question

Which of the following is the correct graph of the solution to the inequality −8 greater than or equal to −5x + 2 > −38? (1 point) number line with an open dot at 2 with shading to the left and another open dot at 8 with shading to the right. number line with an open dot at 8 and at 2 with shading in between. number line with a closed dot on 2 and an open dot on 8 and shading in between. number line with closed dots at 2 and 8 with shading between the 2 and the 8.

Answer 1

−8 greater than or equal to −5x + 2 > −38

writing it out:

-8 ≥ -5x + 2 > -38

subtract 2:

-10 ≥ -5x > -40

add 5x

5x -10 ≥ 0 > 5x - 40

separate into two expressions

5x -10 ≥ 0

5x ≥ 10

x ≥ 2

and

0 > 5x -40

40 > 5x

8 > x

combining

8 > x ≥ 2

so ans is

number line with a closed dot on 2 and an open dot on 8 and shading in between

Answer 2

The inequality should read:

`-8 \geq -5x + 2 > -38`

Subtract 2 from all the terms:

`-10 \geq -5x > -40`

Divide all the terms by -5 to get x by itself (note that you flip the inequality signs as you divide by a negative):

`\boxed{2 \leq x < 8}`

The inequality is 2 ≤ x < 8.

A closed dot represents ≤, and an open dot represents <. Since x can represent all values between 2 and 8, you will shade in between 2 and 8 on the number line. x is greater than or equal to 2, so there will be a closed dot on 2. x is less than 8, so there will be an open dot on 8.

The answer is 'number line with a closed dot on 2 and an open dot on 8 and shading in between'.