Question

Drag each equation to the correct location on the table.

Answer 1

Answer:

1) $3^{x}=2^{x} +1$ ------> 1 solution

2) $3x-2=3^{x} +1$ ------> No solutions

3) $2^{x} -1=4^{x}+3$ ----> No solutions

4) $2x+1=2^{x}$ ----> 2 solutions

5) $(1/2)x+3=3^{x}-1$ ----> 2 solutions

Step-by-step explanation:

we know that

Using a graphing tool

Verify each case

case 1) we have

$3^{x}=2^{x} +1$ -----> equation A

we know that

The equation A can be divided into two equations B and C

$y=3^{x}$ -----> equation B

$y=2^{x} +1$ -----> equation C

The solution of the equation A is the x-coordinate of the intersection point graph equation B and graph equation C

see the attached figure N 1

One point of intersection

therefore

One solution

case 2) we have

$3x-2=3^{x} +1$ -----> equation A

we know that

The equation A can be divided into two equations B and C

$y=3x-2$ -----> equation B

$y=3^{x} +1$ -----> equation C

The solution of the equation A is the x-coordinate of the intersection point graph equation B and graph equation C

see the attached figure N 2

No point of intersection

therefore

No solutions

case 3) we have

$2^{x} -1=4^{x}+3$ -----> equation A

we know that

The equation A can be divided into two equations B and C

$y=2^{x} -1$ -----> equation B

$y=4^{x} +3$ -----> equation C

The solution of the equation A is the x-coordinate of the intersection point graph equation B and graph equation C

see the attached figure N 3

No point of intersection  

therefore

No solutions

case 4) we have

$2x+1=2^{x}$ -----> equation A

we know that

The equation A can be divided into two equations B and C

$y=2x+1$ -----> equation B

$y=2^{x}$ -----> equation C

The solution of the equation A is the x-coordinate of the intersection point graph equation B and graph equation C

see the attached figure N 4

Two point of intersection  

therefore

Two solutions

case 5) we have

$(1/2)x+3=3^{x}-1$ -----> equation A

we know that

The equation A can be divided into two equations B and C

$y=(1/2)x+3$ -----> equation B

$y=3^{x}-1$ -----> equation C

The solution of the equation A is the x-coordinate of the intersection point graph equation B and graph equation C

see the attached figure N 5

Two point of intersection  

therefore

Two solutions