The correct answers are:
#1] A) t = 3
#2] D) Identity
#3] B) c = -6
#4] B) m = 2
Explanation:
#1] 4 - t = 3(t - 1) - 5
First we will use the distributive property on the right hand side:
4 - t = 3t - 31 - 5
4 - t = 3t - 3 - 5
Now we combine like terms on the right hand side:
4 - t = 3t - 8
Add t to each side:
4 - t + t = 3t - 8 + t
4 = 4t - 8
Add 8 to each side:
4 + 8 = 4t - 8 + 8
12 = 4t
Divide both sides by 4:
12/4 = 4t/4
3 = t
#2] 8x - 2(x + 1) = 2(3x - 1)
Use the distributive property on each side:
8x - 2x - 21 = 23x - 21
8x - 2x - 2 = 6x - 2
Combine like terms on the left:
6x - 2 = 6x - 2
Since we have the same thing on each side, this is an identity.
#3] 3(c - 2) = 2(c - 6)
Use the distributive property on each side:
3c - 32 = 2c - 26
3c - 6 = 2c - 12
Subtrat 2c from each side:
3c - 6 - 2c = 2c - 12 - 2c
c - 6 = -12
Add 6 to each side:
c - 6 + 6 = -12 + 6
c = -6
#4] 0.5(m + 4) = 3(m - 1)
Use the distributive property on each side:
0.5m + 0.54 = 3m - 31
0.5m + 2 = 3m - 3
Subtract 0.5m from each side:
0.5m + 2 - 0.5m = 3m - 3 - 0.5m
2 = 2.5m - 3
Add 3 to each side:
2 + 3 = 2.5m - 3 + 3
5 = 2.5m
Divide both sides by 2.5:
5/2.5 = 2.5m/2.5
2 = m
