1). 6 - (5r) = 5r - 3
6 -5r = 5r - 3 (distribute the negative)
-5r = 5r - 3 - 6 (subtract 6 from both sides)
-10r = -9 (subract 5r from both sides and combine like terms)
r = -9/-10 (divide by -10 on both sides)
r = 9/10 (negative divided by negative = positive)
2). 12p - 7 = 3p + 8
12p = 3p + 8 + 7 (add 7 to both sides)
12p - 3p = 15 (subtract 3p from both sides and add like terms)
9p = 15 (combine like terms on left)
p = 15/9 (divide both sides by 9)
3). 10 (-4 + y) = 2y
-40 + 10y = 2y (distribute the 10)
10y = 2y + 40 (add 40 to both sides)
10y - 2y = 40 (subtract 2y from both sides)
8y = 40 (combine like terms)
y = 5 (divide both sides by 8)
4). -(8n - 2) = 3 + 10(1 - 3n)
-8n + 2 = 3 + 10 - 30n (distribute)
-8n = 3 + 10 - 30n - 2 (subtract 2 from both sides)
-8n + 30n = 3 + 10 - 2 (add 30n to both sides)
22n = 11 (combine like terms)
n = 11/22 (divide each side by 22)
n = 1/2 (simplify)
5). 1/4(60 + 165) = 15 + 45
1/4(60) + 1/4(165) = 15 + 45 (distribute 1/4 to numbers inside ())
60/4 + 165/4 = 60 (combine numbers on right)
225/4 = 60 (add fractions together)
0 = 60(4/4) - 225/4 (subtract 225/4)
0 = 240/4 - 225/4 (find common denominator)
0 does not equal 15/4 (subtract)
impossible. (impossible to solve)