45)
E = mc² (solve for "m" by dividing both sides by c²)
E/c² = m
46)
c(a + b) - d = f (to solve for "a"; add "d", divide by "c" and then subtract "b")
c(a + b) = f + d
(a + b) = (f + d)/c
a = (f + d)/c - b
47)
z = πq³h (solve for "h" by dividing both sides by πq³)
z/πq³ = h
48)
(x + y)/z - a = b (solve for "y"; add "a", multiply by "z", and then subtract "x")
(x + y)/z = b + a
(x + y) = z(b + a)
y = z(b + a) - x
53)
5x - 9 = 11x + 3
-9 = 6x + 3 subtracted 5x from both sides
-12 = 6x subtracted 3 from both sides
-2 = x divided both sides by 6
55)
5.4(3k - 12) + 3.2(2k + 6) = -136
16.2k - 64.8 + 6.4k + 19.2 = -136 distributed 5.4 and 3.2
22.6k - 45.6 = -136 added like terms (16.2k + 6.4k and -64.8 + 19.2
22.6k = -90.4 added 45.6 to both sides
k = -4 divided both sides by 22.6
57)
(4/9)y + 5 = (-7/9)y - 8
4y + 45 = -7y - 72 multiplied by 9 to clear the denominator
11y + 45 = -72 added 7y to both sides
11y = -99 subtracted 45 from both sides
y = -9 divided both sides by 11