Question

Solve and graph the inequality |4 – v| < 5.
a. Write the inequality as two inequalities without absolute value.
b. Solve the inequality and write the solution set.
c. Graph the solution on a number line.

Answer 1

Hello @zun and Welcome to OpenStudy! :)

for part a, know that |a - b| < c
becomes a - b < c and a - b > -c

Answer 2

then in part b, (after you split the absolute values)
solve the inequalities like you would a normal equation :)

Answer 3

oh...ok I think I can do b

Answer 4

can you help me with the graph? ^^

Answer 5

sure :D
once you get part b
plot the two points that you ended up with on a number line
then I can guide you on where to shade them ^_^

Answer 6

ok...got it! thank you so much. ^^

Answer 7

you're welcome :)

Answer 8

@jigglypuff314 can you check my answer for me please? ^^ b. 4 – v < 5
4 - v - 4 < 5 - 4
-v < 1
(-1) (-v) > (-1) (1)
v > -1

Answer 9

yes :)
that's one part
and the other part of it is 4 - v > - 5
can you solve for v from that too?

Answer 10

yeah...hold on!

Answer 11

great! :)

Answer 12

now we have v > -1
which means that graph is shaded greater than -1
and v < 9 means that graph is shaded less than 9
where they over lap is where your answer is and where you shade :)

Answer 13

oh...thank you very much!!!! ^^

Answer 14

you're welcome :)