Solving Equations With Variables On Both Sides

1) Solve: -7 - 4c = -c + 8

C = -5

C = -3

C = 3

C = 5

To solve the equation, we need to isolate the variable c. First, we can combine like terms by adding c to both sides of the equation. This gives us -7 - 3c = 8. Next, we can simplify further by adding 7 to both sides, resulting in -3c = 15. To isolate c, we divide both sides of the equation by -3. This gives us c = -5. Therefore, the correct answer is c = -5.

Explanation

To solve the equation, we need to isolate the variable c. First, we can combine like terms by adding c to both sides of the equation. This gives us -7 - 3c = 8. Next, we can simplify further by adding 7 to both sides, resulting in -3c = 15. To isolate c, we divide both sides of the equation by -3. This gives us c = -5. Therefore, the correct answer is c = -5.

2) Solve: -7p = -8p + 9

P = 3/5

P = -9

P = 9

P = -3/5

The equation given is -7p = -8p + 9. To solve for p, we can start by simplifying the equation. By subtracting -8p from both sides of the equation, we get p = 9. Therefore, the correct answer is p = 9.

Explanation

The equation given is -7p = -8p + 9. To solve for p, we can start by simplifying the equation. By subtracting -8p from both sides of the equation, we get p = 9. Therefore, the correct answer is p = 9.

3) Solve: 10t + 10 = -8 + 8t

T = -18

T = -9

T = 18

T = 9

To solve the equation 10t + 10 = -8 + 8t, we need to simplify both sides of the equation. By combining like terms, we get 2t + 10 = -8. Next, we can isolate the variable by subtracting 10 from both sides, resulting in 2t = -18. Finally, we divide both sides by 2 to solve for t, giving us t = -9.

Explanation

To solve the equation 10t + 10 = -8 + 8t, we need to simplify both sides of the equation. By combining like terms, we get 2t + 10 = -8. Next, we can isolate the variable by subtracting 10 from both sides, resulting in 2t = -18. Finally, we divide both sides by 2 to solve for t, giving us t = -9.

4) How many solutions are there for the following equation: -5q - 9 = 4q

No solutions

One solution

Infinitely many solutions

The given equation is a linear equation. To solve it, we can combine like terms and isolate the variable. By adding 5q to both sides, we get -9 = 9q. Dividing both sides by 9, we find that q = -1. Therefore, there is one solution for the equation, which is q = -1.

Explanation

The given equation is a linear equation. To solve it, we can combine like terms and isolate the variable. By adding 5q to both sides, we get -9 = 9q. Dividing both sides by 9, we find that q = -1. Therefore, there is one solution for the equation, which is q = -1.

5) Is this an identity: 5 - 5z = -5z + 5

Yes

No

The given equation is an identity because both sides of the equation are equal when simplified. By rearranging the terms, we can see that 5 - 5z is equal to -5z + 5. This holds true for any value of z, making it an identity.

Explanation

The given equation is an identity because both sides of the equation are equal when simplified. By rearranging the terms, we can see that 5 - 5z is equal to -5z + 5. This holds true for any value of z, making it an identity.

6) How many solutions are there for the following equation: -4c = 8 - 4c

No solutions

One solution

Infinitely many solutions

The equation -4c = 8 - 4c can be simplified to 0 = 8, which is not possible. This means that there are no values of c that satisfy the equation, leading to the conclusion that there are no solutions.

Explanation

The equation -4c = 8 - 4c can be simplified to 0 = 8, which is not possible. This means that there are no values of c that satisfy the equation, leading to the conclusion that there are no solutions.