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24-25 ARMY AIR FORCES (2) Example: Evaluate a[(a-b)+c(a²-c)-d(a-c²)] when a=2, b=3, c=4, d=6. Solution: 2[(2-3)+4(2²-4)-6(2-4²)]= 2[-1+4(0)-6(-14)]= 2[-1+0+84]=2[83]=166 Answer. b. Exercises.–– Evaluate the following if x=3, y=2, z=5. (1)x(y+2)(3y+x) (2)4(x²-y) + y²(z-y) 40 Answer. (3)(y-3x) + z(y-x) (4)x(x+y) + z²+x(y-3) 37 Answer. (5)0[x+y(z-7)+4]-7 (6)z-x/z-y 2/3 Answer. (7)x+y/y 25.Equations. - a. An equation is a statement of equality between any two quantities. Thus, in reality, all formulas are equations. In most equations that are used, there is an unknown quantity for which a value sought. To find this, certain rules must be followed: (1) Equal quantities may be added to both sides of the equation. Example: x -4= 7 +4= +4 _____________ x = 11 (2)Equal quantities may be sybtracted from both sides of the equation. Example: x +2 = 5 -2 = -2 ______________ x = 3 (3)Both sides of the equation may be multiplied by the same quantity. Example: x/2 = 4 x = 4.2 x = 8 (4) Both sides may be divided by the same quantity (zero excepted). Example: 3x= 12 3x/3 = 12/3 x = 4 40