Question

The table below shows two equations:


Equation 1 |2x − 3| + 5 = 4
Equation 2 |5x + 3| − 10 = 3


Which statement is true about the solution to the two equations?
a.) Equation 1 and equation 2 have no solutions.
b.) Equation 1 has no solution, and equation 2 has solutions x = 2, −3.2.
c.) The solutions to equation 1 are x = 1, 2, and equation 2 has no solution.
d.) The solutions to equation 1 are x = 1, 2, and equation 2 has solutions x = 2, −3.2.

Answer 1

Hi
Welcome to openstudy :-)
Any ideas on where to start?

Answer 2

@pooja195 so far all I have done is solve for one solution for |2x-3|+5=4

Answer 3

Ok good, that's correct.
Try out the 2nd one
|5x + 3| − 10 = 3

Answer 4

@pooja195
|5x+3|-10-10=3-10
5x+3=-7
5x+3-3=-7-3
5x=-10
5x/5=-10/5
x=-2

Answer 5

\(\color{#0cbb34}{\text{Originally Posted by}}\) @Nefxrious
@pooja195
|5x+3|-10-10=3-10
5x+3=-7
5x+3-3=-7-3
5x=-10
5x/5=-10/5
x=-2
\(\color{#0cbb34}{\text{End of Quote}}\)
We need to ADD 10 because we want to cancel it out
\[\huge~\rm~\bf~ |5x+3|-10+10=3+10\]
try now :-)

Answer 6

@pooja195 oops! sorry!
|5x+3|-10+10=3+10
5x+3=13
5x+3-3=13-3
5x=10
5x/5=10/5
x=2

Answer 7

Good now
5x+3=-13 <---absolute values have a negative and positive solution so we have to do it with -13 as well

Answer 8

@pooja195
5x+3-3=-13-3
5x=-10
5x/5=-10/5
x=-2

Answer 9

-13-3=?

Answer 10

@pooja195
5x+3-3=-13-3
5x=-16
5x/5=-16/5
x=-3.2?

Answer 11

Perfect :D
So our answer choice would be...?

Answer 12

@pooja195 D right?

Answer 13

The first one has no solutions

Answer 14

@pooja195 when I solved for the first one I got 1

Answer 15

my bad i meant one solution sorry

Answer 16

which answer choice matches the answers we got?

Answer 17

@pooja195 so it would be D correct?

Answer 18

d.) The solutions to equation 1 are x = 1, 2, and equation 2 has solutions x = 2, −3.2.
The solution to equation 1 was one solution this does not match

Answer 19

@pooja195 but there is no answer that says equation one only has 1 solution

Answer 20

Equation 1 has: No solutions

Equation 2: 2 and -3.2
match the options.

Answer 21

@pooja195 how come it doesn't have a solution if it has 1 as a solution?

Answer 22

Not sure what you are trying to say.
Step 1: Add -5 to both sides.
|2x−3|+5+−5=4+−5
|2x−3|=−1
Step 2: Solve Absolute Value.
|2x−3|=−1
No solutions. (Absolute value cannot be less than 0.)

Answer 23

a.) Equation 1 and equation 2 have no solutions.
Do they both have no solution?

Answer 24

@pooja195 ohhh I got a positive 1 I see where you are getting at

Answer 25

Yes :-)

Answer 26

so the answer is...?

Answer 27

@pooja195 B

Answer 28

good ::-)

Answer 29

@pooja195 do you think you can help me with something else?

Answer 30

sure ill try

Answer 31

@pooja195 Henry is taking a medicine for a common cold. The table below shows the amount of medicine f(t), in mg, that was present in Henry's body after time t:


t (hours) 1 2 3 4 5
f(t) (mg) 282 265.08 249.18 234.22 220.17


Greg was administered 300 mg of the same medicine. The amount of medicine in his body f(t) after time t is shown by the equation below:

f(t) = 300(0.88)t

Which statement best describes the rate at which Henry's and Greg's bodies eliminated the medicine?
a.) Henry's body eliminated the antibiotic faster than Greg's body.
b.) Henry's body eliminated the antibiotic at the same rate as Greg's body.
c.) Henry's body eliminated the antibiotic at half of the rate at which Greg's body eliminated the antibiotic.
d.) Henry's body eliminated the antibiotic at one-fourth of the rate at which Greg's body eliminated the antibiotic.

Answer 32

@Nefxrious im sorry about @Jaynator495 's behavior if you can please repost the question :-) im not sure about this one

Answer 33

@pooja195 okay thank you for everything! I suppose @Jaynator495 deleted their response since it disappeared

Answer 34

yes they did ;0
yw^-^

Answer 35

I nearly Crashed entering that... ._.
But anywho xD