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 p^{2} + 5p= 0 Solution: p^{2} + 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 |
28)
Solve 5x^{2} - x= 0 Solution: 5x^{2} - 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 15s^{2} - 20s= 0 15s^{2} - 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 x^{2} - 36= 0 x^{2} - 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 9y^{2} - 1= 0 9y^{2} - 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 16z^{2} - 25 = 0 16z^{2} - 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 z^{2} = 25 z^{2} = 25 z^{2} - 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 9y^{2} = 64 9y^{2} = 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. |