Question

3(q+2)-2(q+3)=0

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve this equation, we need to distribute the numbers outside the parentheses.

3(q) + 3(2) - 2(q) - 2(3) = 0
3q + 6 - 2q - 6 = 0

Now, combine like terms on each side of the equation:

3q - 2q + 6 - 6 = 0
q = 0

Therefore, the solution to the equation 3(q+2) - 2(q+3) = 0 is q = 0.

Answer 2

8w-10=3w+15

Answer 3

[AI-generated answer — Bot GPT 3.5]

To solve this equation, we need to isolate the variable w.

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

8w - 10 = 3w + 15

Next, we need to get all the w terms on one side and the constant terms on the other side. We can do this by subtracting 3w from both sides and adding 10 to both sides:

8w - 3w - 10 = 3w - 3w + 15 + 10
5w - 10 = 25

Now, we can isolate w by adding 10 to both sides:

5w - 10 + 10 = 25 + 10
5w = 35

Finally, we divide both sides by 5 to solve for w:

5w/5 = 35/5
w = 7

Therefore, the solution to the equation 8w - 10 = 3w + 15 is w = 7.

Answer 4

5(2n-3)=7(2n-5)+8

Answer 5

[AI-generated answer — Bot GPT 3.5]

To solve this equation, we first need to distribute the numbers outside the parentheses:

5(2n) - 5(3) = 7(2n) - 7(5) + 8
10n - 15 = 14n - 35 + 8

Now, we simplify the equation by combining like terms:

10n - 15 = 14n - 27

Next, let's isolate the variable 'n' by getting all the 'n' terms on one side and the constant terms on the other side. We can do this by subtracting 10n from both sides:

10n - 10n - 15 = 14n - 10n - 27
-15 = 4n - 27

Then, add 27 to both sides to simplify further:

-15 + 27 = 4n - 27 + 27
12 = 4n

Finally, divide by 4 to solve for 'n':

12 / 4 = n
n = 3

Therefore, the solution to the equation 5(2n-3) = 7(2n-5) + 8 is n = 3.

Answer 6

6(3a-2)=3(a+5)+3

Answer 7

[AI-generated answer — Bot GPT 3.5]

To solve this equation, we first need to distribute the numbers outside the parentheses:

6(3a) - 6(2) = 3(a) + 3(5) + 3
18a - 12 = 3a + 15 + 3

Now, we simplify the equation by combining like terms:

18a - 12 = 3a + 18

Next, let's isolate the variable 'a' by getting all the 'a' terms on one side and the constant terms on the other side. We can do this by subtracting 3a from both sides:

18a - 3a - 12 = 3a - 3a + 18
15a - 12 = 18

Next, add 12 to both sides to simplify further:

15a - 12 + 12 = 18 + 12
15a = 30

Finally, divide by 15 to solve for 'a':

15a / 15 = 30 / 15
a = 2

Therefore, the solution to the equation 6(3a-2) = 3(a+5) + 3 is a = 2.