Question

4x-9+6x=7+2x+3

identity
no solution

Answer 1

[AI-generated answer — Bot GPT 3.5]

To determine if this equation is an identity or has no solution, we need to simplify it further and see if both sides are equal or not.

Starting with the given equation: 4x - 9 + 6x = 7 + 2x + 3

Combining like terms on both sides:
10x - 9 = 2x + 10

Subtracting 2x from both sides:
10x - 2x - 9 = 2x - 2x + 10
8x - 9 = 10

Adding 9 to both sides:
8x - 9 + 9 = 10 + 9
8x = 19

Dividing both sides by 8:
(8x)/8 = 19/8
x = 19/8

Since x has a numerical value, this equation has a solution. Therefore, the equation is not an identity and does not fall under the category of having no solution.

Answer 2

[AI-generated answer — Step-by-Step Bot]

To determine if the equation 4x-9+6x=7+2x+3 is an identity or has no solution, we need to simplify both sides of the equation and then compare them.

First, let's simplify the equation by combining like terms on both sides:

4x-9+6x = 7+2x+3

Combining like terms gives us:

10x - 9 = 10 + 2x

Next, let's get all the x terms on one side of the equation by subtracting 2x from both sides:

10x - 2x - 9 = 10 + 2x - 2x

Simplifying further, we have:

8x - 9 = 10

Now, let's get the constant term on the other side of the equation by adding 9 to both sides:

8x - 9 + 9 = 10 + 9

Simplifying, we get:

8x = 19

Finally, divide both sides of the equation by 8 to solve for x:

(8x)/8 = 19/8
x = 19/8

Therefore, the equation 4x-9+6x=7+2x+3 has a solution, and the value of x is 19/8. It does not have no solution.

Answer 3

[AI-generated answer — Explain Bot]

To determine whether the given equation is an identity, we need to simplify both sides of the equation and check if they are equal for all values of 'x'.

Let's solve the equation step by step:

Given equation: 4x - 9 + 6x = 7 + 2x + 3

First, combine the like terms on both sides of the equation:
(4x + 6x) - 9 = (2x + 7) + 3

Simplifying further:
10x - 9 = 2x + 10

Next, we want to isolate the 'x' term. To do this, we can subtract 2x from both sides of the equation:
10x - 2x - 9 = 2x - 2x + 10

Simplifying further:
8x - 9 = 10

To isolate the 'x' term completely, we can add 9 to both sides of the equation:
8x - 9 + 9 = 10 + 9

Simplifying further:
8x = 19

Finally, to solve for 'x', divide both sides of the equation by 8:
(8x)/8 = 19/8

Simplifying further:
x = 19/8

Now, we have found a specific value for 'x', which means the equation has a solution. Therefore, the given equation is not an identity.

Since the given equation has at least one solution, we can conclude that it does not have "no solution".