1. Solve the equation: 4 - t = 3(t - 1) - 5
A. 3
B. 6
C. No solution
D. Identity
2. 8x - 2(x + 1) = 2(3x - 1)
A. 0
B. 2
C. No solution
D. Identity
3. 3(c - 2) = 2(c - 6)
A. 2
B. -6
C. No solution
D. Identity
4. 0.5(m + 4) = 3(m - 1)
A. -2
B. 2
C. No solution
D. Identity
The answers to the equations are as follows:
1. Solve the equation: 4 - t = 3(t - 1) - 5
Simplify both sides of the equation:
4 - t = 3t - 3 - 5
Combine like terms:
4 - t = 3t - 8
Add t to both sides:
4 = 4t - 8
Add 8 to both sides:
12 = 4t
Divide by 4:
t = 3
Therefore, the solution to the equation is A. 3.
2. Solve the equation: 8x - 2(x + 1) = 2(3x - 1)
Simplify both sides of the equation:
8x - 2x - 2 = 6x - 2
Combine like terms:
6x - 2 = 6x - 2
This is an identity, which means that the equation is true for all x.
Therefore, the solution to the equation is D. Identity.
3. Solve the equation: 3(c - 2) = 2(c - 6)
Distribute:
3c - 6 = 2c - 12
Subtract 2c from both sides:
c - 6 = -12
Add 6 to both sides:
c = -6
Therefore, the solution to the equation is B. -6.
4. Solve the equation: 0.5(m + 4) = 3(m - 1)
Distribute:
0.5m + 2 = 3m - 3
Subtract 0.5m from both sides:
2 = 2.5m - 3
Add 3 to both sides:
5 = 2.5m
Divide by 2.5:
m = 2
Therefore, the solution to the equation is B. 2.
To solve these equations step-by-step, let's start with the first one:
1. Solve the equation: 4 - t = 3(t - 1) - 5
Distribute on the right side of the equation:
4 - t = 3t - 3 - 5
Combine like terms:
4 - t = 3t - 8
Add "t" on both sides to isolate the variable:
4 = 4t - 8
Now, add 8 to both sides:
12 = 4t
Divide by 4 on both sides to solve for "t":
t = 3
Therefore, the answer is A. 3.
Moving on to the second equation:
2. 8x - 2(x + 1) = 2(3x - 1)
Distribute on the left side:
8x - 2x - 2 = 6x - 2
Combine like terms:
6x - 2 = 6x - 2
The equation simplifies to 0 = 0.
Since the variable has canceled out and both sides are equal, this equation is a D. Identity.
Now, let's work on the third equation:
3. 3(c - 2) = 2(c - 6)
Distribute on the left side:
3c - 6 = 2c - 12
Subtract 2c on both sides to isolate the variable:
c - 6 = -12
Add 6 to both sides:
c = -6
Therefore, the answer is B. -6.
Lastly, let's solve the fourth equation:
4. 0.5(m + 4) = 3(m - 1)
Distribute on the left side:
0.5m + 2 = 3m - 3
Subtract 0.5m on both sides to isolate the variable:
2 = 2.5m - 3
Add 3 on both sides:
5 = 2.5m
Divide by 2.5 to solve for "m":
m = 2
Therefore, the answer is B. 2.