Question

Graph the solution of the open sentence. 8 < 2b or 2b + 15 < 5


Number line -5 to +5 in single-integer increments - assessment graphic


Number line showing range from negative three to three The left end point is an open circle halfway between negative one and zero. There is a closed dot at three, and a ray points past three.


Number line showing range from negative four to four. There are two rays on the graph. The first has a right end point with a closed dot at negative two with a ray pointing left past negative four. The second has a left end point with an open circle at three with a ray pointing right past four.


Number line showing range from negative eight to eight. There are two rays on the graph. The first has a right end point with an open circle halfway between negative six and negative four with a ray pointing left past negative eight. The second has a left end point with an open circle at four with a ray pointing right past eight.

Answer 1

I will not do the whole thing but I will demonstrate how to approach this problem using *one* of the inequalities

8 < 2b

Let’s flip it around to make it easier to work with

2b < 8

If you divide both sides by 2 you get

b < 4

Since we have < or > we use an open circle on 4. To represent b being all values less than 4, we draw a line to the left, towards the negative numbers, on the number line

Can you try doing the other inequality on your own?