Q:

# Which of the following is the correct graph of the solution to the inequality −8 greater than or equal to −5x + 2 &gt; −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.

Accepted Solution

A:
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'.