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Question

1. The cube of ℎ gives 8.

2. 𝑥 reduced by one-fifth is equal to 6.

3. 5 decreased by 𝑧 is one-third.

4. One-half plus 𝑘 is 4.

5. 5 divided by 𝑡 gives 7.

6. The quotient of 𝑏 and thrice of 𝑎 is equal to 5

7. The fourth power 𝑐 is the same as 16 decreased by twice of 𝑏.

8. The sum of 4 and twice of 𝑥 is the product of 𝑥 and 𝑦.

9. 5 is equal to the product of 𝑥 and the sum of 3 and 𝑥.

10. 𝑥 reduced by 1 is equal to twice of 𝑦.

Answer 1

1 h^3 = 8

h=2 is one solution, but with a 3rd degree equation, there are 3 solutions. the other two are imaginary.

factor h^3-8= (h-2)(h^2 +2h +4) =0 and set each factor =0

h-2=0, h=2

h^2 +2h+4 = 0

complete the square

h^2 +2h +1 =-4+1 =-3

(h+1)^2 = -3

h+1 = sqr(-3)

h= -1 + or - isqr3

2 x- 1/5 = 6

x= 6 + 1/5 = 31/5

x= 31/5 = 6.2

3 5-z = 1/3

-z = 1/3 -5

z = 5-1/3 = 4 2/3 or 4.666...

4 1/2 k + 4 = 12

k/2 = 12-4 = 8

k = 16

5 5/t = 7

t= 5/7

6 b/3a = 5

b=15a

or 3a =5/b

a =5/3b

7 c^4 = 16 -2b

c= 4th root of (16-2b) = (16-2b)^(1/4)

or 2b = 16-c^4

b = 8 -c^4/2

8 4+2x = xy

y = 4/x +2

or

xy-2x =-4

x(y-2) =-4

x= -4/(y-2) = 4/(2-y)

9 5 = x(x+3)

5=x^2 +3x

x^2 +3x -5 = 0

x=-3/2 + or - (1/2)sqr(9-4(-5))

= -3/2 + or - (1/2)sqr29

10 x-1 = 2y

y= (x-1)/2 = x/2 -1/2

or x = 2y+1