solve the compound inequality 4u-3>21 and 3u+6> or =15

Question

write the solution in interval notion.

Answer 1

Start with 4u-3>21 add 3 to both sides

4u > 24 divide both sides by 4

u > 6

Now solve

3u+6> or =15 subtract 6 from both sides

3u > 9 divide by 3

u >3

Now you have u > 6 and u > 3, we are looking for all numbers that are in BOTH parts of this, or where the graphs overlap. So u > 6.

Answer 2

4u - 3 > 21 3u + 6 >= 15

+ 3 + 3 - 6 -6

---------------- ----------------

4u > 24 3u >= 9

--- ---- ---- ----

4 4 3 3

becomes becomes

u > 6 u >= 3

So in interval notation, we have

[3,6) U (6,∞).

There is a bracket on the 3 because we are including 3. Hence,the equal sign on >=.

Hope this helps!