Question

Drag each equation to the correct location on the table.

Determine the number of solutions in each equation. Then place each equation in the box that corresponds to its number of solutions.

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

Answer 2

The categories of the equations are:

• No solution: 3x - 2 = 3ˣ + 1 and 2ˣ - 1 = 4ˣ + 3
• One solution: 3ˣ = 2ˣ + 1
• Two solutions: (1/2)x + 3 = 3ˣ - 1 and 2x + 1 = 2ˣ

How to categorize the equations?

To categorize the equations, we simply split the single equation to two equations, and then plot the graph of the two equations.

The point of intersection between the lines/curves of the equations would determine the number of solutions.

Using the above highlights, we have:

• No solution: 3x - 2 = 3ˣ + 1 and 2ˣ - 1 = 4ˣ + 3 because there is no point of intersection
• One solution: 3ˣ = 2ˣ + 1 because there is one point of intersection
• Two solutions: (1/2)x + 3 = 3ˣ - 1 and 2x + 1 = 2ˣ because there are two point of intersections

See attachment for the graphs

Read more about equation solutions at:

https://brainly.com/question/11851289

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