Question

Which of the following is the correct graph of the compound inequality 4p + 1 > −7 or 6p + 3 < 33?. . A.a number line with open circles at -2 and 5 with shading in between.. . B.number line with open dots at ¨C2 and 5 and shading to the right of 5 and to the left of ¨C2.. . C.number line with shading everywhere.. . D.number line with open dot at ¨C2 and a closed dot at 5 and shading in between.

Answer 1

Option: A is the correct answer.

A. a number line with open circles at -2 and 5 with shading in between.

Explanation:

We are given a system of linear inequality in terms of variable ''p'' as:

(1)
`4p+1>-7`

on subtracting -1 from both side of the inequality we get:

`4p>-8`

Now on dividing both side of the inequality by 4 we get:

`p>-2`

Hence, the region that is obtained is:

(-2,∞)

(2)
`6p+3<33`

on subtracting -3 from both side of the inequality we get:

`6p<30`

Now on dividing both side of the inequality by 5 we get:

`p<5`

Hence, the region that is obtained is:

(-∞,5)

Hence, the common region that is obtained by both the inequalities is:

(-2,5)

i.e. the graph will be a number line with open circle both at -2 and 5 and shading in between them.

Answer 2

break it into 2 inequalities

-13 > -5x + 2 and -5x + 2 > -28 -13-2 > -5x +2-2 -5x > -30 -15 > -5x -5x/(-5) < (-30)/(-5) 3<x x < 6 x>3
Combine the 2 solutions , you'll get 3<x<6
Mark answer on the number line Since it is 'greater than' the 'circle' should not be blacken Perhaps you can try to draw the number line now?