MTH 030 -- Elementary Algebra -- Exercise Solutions
Section:
5.5

15)  Solve (x - 2)(x + 3) = 0
       Solution:  
(x - 2)(x + 3) = 0
if and only if x - 2 = 0 or x + 3 = 0
so x = 2 and x = -3 are solutions to the original equation.
ab = 0 if and only if a = 0 or b = 0

The solution of an equation of the form
x + k = 0 is x = - k    (add - k to both sides)
16)  Solve (x - 3)(x - 2) = 0
       Solution:  
(x - 3)(x - 2) = 0
if and only if x - 3 = 0 or x - 2 = 0
so x = 3 and x = 2 are solutions to the original equation.
ab = 0 if and only if a = 0 or b = 0

The solution of an equation of the form
x + k = 0 is x = - k    (add - k to both sides)
18)  Solve (3h - 4)(h + 1) = 0
       Solution:  
(3h - 4)(h + 1) = 0
if and only if 3h - 4 = 0 or h + 1 = 0
so x = 4/3 and x = -1 are solutions to the original equation.
ab = 0 if and only if a = 0 or b = 0
The solution of an equation of the form
ax + k = 0 is x = - k/a    (add - k to both sides then divide both sides by a)
20)  Solve (x + 2)(x + 3)(x - 4) = 0
       Solution:  
(x + 2)(x + 3)(x - 4)= 0
if and only if x - 2 = 0 or x + 3 = 0 or x - 4 = 0
so x = - 2 and x = -3 and x = 4 are solutions to the original equation.
ab = 0 if and only if a = 0 or b = 0

The solution of an equation of the form
x + k = 0 is x = - k    (add - k to both sides)
22)  Solve x(x + 5) = 0
       Solution:  
x(x + 5) = 0
if and only if x = 0 or x + 5 = 0
so x = 0 and x = -5 are solutions to the original equation.
ab = 0 if and only if a = 0 or b = 0

The solution of an equation of the form
x + k = 0 is x = - k    (add - k to both sides)
24)  Solve x(5x + 7) = 0
       Solution:  
x(5x + 7) = 0
if and only if x = 0 or 5x + 7 = 0
so x = 0 or x = -7/5 are solutions to the original equation.
ab = 0 if and only if a = 0 or b = 0
The solution of an equation of the form
ax + k = 0 is x = - k/a    (add - k to both sides then divide both sides by a)
26)  Solve p2 + 5p= 0
       Solution:  
p2 + 5p = 0 if and only if p(p + 5)= 0
if and only if p = 0 or p + 5 = 0
so p = 0 and p = -5 are solutions to the original equation.

Factor out the common factor
ab = 0 if and only if a = 0 or b = 0
The solution of an equation of the form
x + k = 0 is x = - k    (add - k to both sides)

28)  Solve 5x2 - x= 0
       Solution:  
5x2 - x= 0 if and only if x(5x - 1) = 0
if and only if x= 0 or 5x - 1 = 0
so x = 0 and x = 1/5 are solutions to the original equation.
Factor out the common factor
ab = 0 if and only if a = 0 or b = 0
The solution of an equation of the form
ax + k = 0 is x = - k/a    (add - k to both sides then divide both sides by a)
30)  Solve 15s2 - 20s= 0
 
15s2 - 20s= 0
5s(3s - 4) = 0
5s= 0 or 3s - 4 = 0
so s= 0 and s = 4/3 are solutions to the original equation.
32)  Solve x2 - 36= 0
 
x2 - 36= 0
(x + 6)(x - 6) = 0
x + 6 =0 or x - 6 = 0
so x = -6 and x = 6 are solutions to the original equation.
34)  Solve 9y2 - 1= 0
 
9y2 - 1= 0
(3y - 1)(3y + 1) = 0
3y - 1 = 0 or 3y + 1= 0
so y = 1/3 and x = -1/3 are solutions to the original equation.
36)  Solve 16z2 - 25 = 0
 
16z2 - 25= 0
(4z + 5)(4z - 5) = 0
4z + 5 =0 or 4z - 5 = 0
so z = -5/4 and x = 5/4 are solutions to the original equation.
38)  Solve z2 = 25
 
z2 = 25
z2 - 25 = 0
(z - 5)(z + 5) = 0
z - 5 = 0 or z + 5= 0
so z = 5 and z = -5 are solutions to the original equation.
40)  Solve 9y2 = 64
 
9y2 = 64
9y2 - 64 = 0
(3y + 8)(3y - 8) = 0
3y + 8 =0 or 3y - 8 = 0
so x = -8/3 and x = 8/3 are solutions to the original equation.