# Solving Equations With Variables On Both Sides

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• 1.

• 2.

### Solve:  -7 - 4c = -c + 8

• A.

C = -5

• B.

C = -3

• C.

C = 3

• D.

C = 5

A. 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.

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• 3.

### Solve:  -7p = -8p + 9

• A.

P = 3/5

• B.

P = -9

• C.

P = 9

• D.

P = -3/5

C. 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.

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• 4.

### Solve:  10t + 10 = -8 + 8t

• A.

T = -18

• B.

T = -9

• C.

T = 18

• D.

T = 9

B. 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.

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• 5.

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

• A.

No solutions

• B.

One solution

• C.

Infinitely many solutions

A. 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.

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• 6.

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

• A.

No solutions

• B.

One solution

• C.

Infinitely many solutions

B. One solution
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.

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• 7.

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

• A.

Yes

• B.

No

A. Yes
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.

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