1 answer:
A: Solve for r:
6 r + 6 r - 1 = 11
Grouping like terms, 6 r + 6 r - 1 = (6 r + 6 r) - 1:
(6 r + 6 r) - 1 = 11
6 r + 6 r = 12 r:
12 r - 1 = 11
Add 1 to both sides:
12 r + (1 - 1) = 1 + 11
1 - 1 = 0:
12 r = 11 + 1
11 + 1 = 12:
12 r = 12
Divide both sides of 12 r = 12 by 12:
(12 r)/12 = 12/12
12/12 = 1:
r = 12/12
12/12 = 1:
Answer: r = 1
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B:
Solve for v:
8 = 8 v - 4 (v + 8)
-4 (v + 8) = -4 v - 32:
8 = 8 v + -4 v - 32
Grouping like terms, 8 v - 4 v - 32 = (8 v - 4 v) - 32:
8 = (8 v - 4 v) - 32
8 v - 4 v = 4 v:
8 = 4 v - 32
8 = 4 v - 32 is equivalent to 4 v - 32 = 8:
4 v - 32 = 8
Add 32 to both sides:
4 v + (32 - 32) = 32 + 8
32 - 32 = 0:
4 v = 8 + 32
8 + 32 = 40:
4 v = 40
Divide both sides of 4 v = 40 by 4:
(4 v)/4 = 40/4
4/4 = 1:
v = 40/4
The gcd of 40 and 4 is 4, so 40/4 = (4×10)/(4×1) = 4/4×10 = 10:
Answer: v = 10
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C: x+4/3=2
x=(2-4)/3
x=(6/3)-4/3
x=(6-4)/3
x=2/3
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