Question

Help solve:
3(t+5)-1>t-2(1-t)

A.) all real numbers
B.) no solution
C.) (t:t>-16)
D.) (t:t>0)

Answer 1

also.... explain to me what all real numbers mean and no solution...anyone please help!

Answer 2

callisto help

Answer 3

what does 3(t+5) distribute to

Answer 4

thats how the question is written... it doesnt give the value of t

Answer 5

3(t+5)

3*t+3*5 ... Distribute here

3t + 15 ... Multiply

Answer 6

So 3(t+5) distributes to 3t + 15

Answer 7

yeah i know that, but look at the answers. im not sure what it was be?

Answer 8

*would

Answer 9

alright, then what does -2(1-t) distribute to

Answer 10

-2 + 2t

Answer 11

So we have this so far


3(t+5)-1>t-2(1-t)

3t+15-1>t-2+2t

Answer 12

now combine like terms

Answer 13

3t-14>3t-2

Answer 14

good, now what's next?

Answer 15

im not sure

Answer 16

Can we add or subtract anything from both sides?

Answer 17

yeah we can add a two to both sides... but can we subtract the 3t even though it would cancel it out?

Answer 18

I'm leaning towards subtracting 3t from both sides (you can add 2, but that's not really relevant)

Answer 19

how do u get 3t +14?

Answer 20

oh my bad, made a typo

Answer 21

i didn't mean to type 3t - 14

Answer 22

so what is it exactly?

Answer 23

3t+14>3t-2

3t+14 -3t > 3t-2 -3t ... Subtract 3t from both sides

14 > -2 ... Subtract

Answer 24

What do you notice about the last inequality?

Answer 25

for some reason, i glossed over when you wrote 3t-14, it should be 3t+14

Answer 26

14 is greater than -2

Answer 27

is that always true, sometimes true, or never true

Answer 28

its true

Answer 29

what does all real numbers mean?

Answer 30

basically any number you can think of is a real number

Answer 31

always true

Answer 32

you'll learn about numbers that are known as complex numbers and these numbers aren't real numbers

Answer 33

but that's later down the road

Answer 34

so 3(t+5)-1>t-2(1-t) is always true

Answer 35

since so 3(t+5)-1>t-2(1-t) is always true, this means any real number satisfies the inequality

Answer 36

So the answer is choice A) all real numbers

Answer 37

ok can u help me with another question really quick... i think u would be a good help

Answer 38

Here's the full step by step solution (in one complete post). This will be for you to take notes from.


3(t+5)-1>t-2(1-t)

3t+15-1>t-2+2t

3t+14>3t-2

3t+14 -3t > 3t-2 -3t ... Subtract 3t from both sides

14 > -2 ... Subtract


Since the last inequality is always true (regardless of the value of t), this means that the original inequality is always true (regardless of the value of t)


So any real number satisfies the inequality 3(t+5)-1>t-2(1-t)


So the answer is choice A) all real numbers

Answer 39

whats your other question

Answer 40

actually 2 questions:
absolute value of (3p-3/5)>6/5

Answer 41

| 3p-3/5 | > 6/5

breaks down to

3p-3/5 > 6/5 or 3p-3/5 < -6/5

From here, solve each equation for p to get your two answers

Answer 42

ok

Answer 43

let me know what you get

Answer 44

p>8/15 and ...

Answer 45

close, but it's not 8

Answer 46

oh typo...9/15

Answer 47

y do you change the 6/5 to negative and positive?

Answer 48

good fix

Answer 49

you can then reduce 9/15 to what?

Answer 50

Because |x| > k implies that

x > k or x < -k

for some positive number k

Answer 51

1/5 and the other is 1/5

Answer 52

both are 1/5?

Answer 53

no 3/5 and -1/5 i think

Answer 54

good, that's part of it

Answer 55

how do the signs fit in?

Answer 56

p>3/5 and p<1/3

Answer 57

first part is correct, second is not

Answer 58

btw, you say "or" instead of "and"

Answer 59

-1/5

Answer 60

better, so its

p > 3/5 or p < -1/5

Answer 61

k thx... i dont need help on the other question cuz i understand it now... ur a good helper... help me next time!! lol

Answer 62

I'm glad you think so and that it's starting to click for you