Solve the equation

Question

4 - t = 3 (t-1) - 5

A. 3
B. 6
C. No solution
D. Identity

Answer 1

To solve the equation, we can start by simplifying both sides:

4 - t = 3(t - 1) - 5

First, distribute 3 to (t - 1):

4 - t = 3t - 3 - 5

Combine like terms:

4 - t = 3t - 8

To isolate t, we can move all terms with t to one side:

-t - 3t = -8 - 4

-4t = -12

Finally, divide both sides by -4:

t = 3

The solution to the equation is t = 3.

Therefore, the correct answer is A. 3.

Answer 2

8x - 2 (x + 1) = 2 (3x - 1)

A. 0
B. 2
C. No solution
D: identity

Answer 3

To solve the equation, we can start by simplifying both sides:

8x - 2(x + 1) = 2(3x - 1)

First, distribute 2 to (x + 1) and 2 to (3x - 1):

8x - 2x - 2 = 6x - 2

Combine like terms:

6x - 2 = 6x - 2

Notice that both sides of the equation are already identical. This means that the equation is an identity.

Therefore, the correct answer is D. identity.

Answer 4

3 (c - 2) = 2 (c - 6)

A. 2
B. -6
C. No solution
D. Identity

Answer 5

To solve the equation, we can start by distributing 3 to (c - 2) and distributing 2 to (c - 6):

3(c - 2) = 2(c - 6)

This simplifies to:

3c - 6 = 2c - 12

Next, we can move all terms with c to one side by subtracting 2c from both sides:

3c - 2c - 6 = 2c - 2c - 12

This simplifies to:

c - 6 = -12

Finally, we can isolate c by adding 6 to both sides:

c - 6 + 6 = -12 + 6

This simplifies to:

c = -6

The solution to the equation is c = -6.

Therefore, the correct answer is B. -6.

Answer 6

0.5(m+4) = 3(m-1)
A. -2
B. 2
C. No solution
D. Identity

Answer 7

To solve the equation, we can start by distributing 0.5 to (m + 4) and distributing 3 to (m - 1):

0.5(m + 4) = 3(m - 1)

This simplifies to:

0.5m + 2 = 3m - 3

Next, we can move all terms with m to one side by subtracting 0.5m from both sides:

0.5m - 0.5m + 2 = 3m - 0.5m - 3

This simplifies to:

2 = 2.5m - 3

Now, let's isolate m by adding 3 to both sides:

2 + 3 = 2.5m - 3 + 3

This simplifies to:

5 = 2.5m

Finally, we divide both sides by 2.5 to solve for m:

5/2.5 = (2.5m)/2.5

This simplifies to:

2 = m

The solution to the equation is m = 2.

Therefore, the correct answer is B. 2.