Question

Using appropriate properties, find the value. Also write the name of the property used. (3 Marks)
a) 2/3 X (-5/7) + 7/3 + 2/3 X (-2/7)
b) ( 1/2x -1/7) + (1/2x 6)

Answer 1

Answer:

a) 2/3 X (-5/7) + 7/3 + 2/3 X (-2/7)

y=55/21 or 2 13/21

PREMISES

-2/3×(-5/7)+7/3+2/3×(-2/7)=y

CALCULATIONS

y=[(-2/3)(-5/7)]+7/3+[(2/3)(-2/7)]

y=(-2×-5)/(3×7)+7/3+(2×-2)/(3×7)

y=10/21+7/3+-4/21 (Convert all fractions to the LCD=21 to simplify the math)

y=(10/21+49/21)+-4/21

y=(10+49)/21+-4/21

y=59/21+-4/21

y=(59–4)/21

y=55/21

y=

55/21 or 2 13/21 as a mixed fraction

PROOF

If y=55/21, then the equations

y=59/21–4/21

55/21=59/21–4/21

55/21=(59–4)/21 and

55/21=55/21 establish that y=55/21 is a solution to the equation (-2/3)(-5/7)+7/3+(2/3)(-2/7)=y

C.H.

b) ( 1/2x -1/7) + (1/2x 6)

2x−1

2x−6

>1

2x−1

2x−6−2x+1

>0

2x−1

−5

>0

2x−1

5

<0

2x−1<0

=>x<

2

1

Answer 2

Answer:

Carbon dioxide is an acidic colorless gas with a density about 53% higher than that of dry air. Carbon dioxide molecules consist of a carbon atom covalently double bonded to two oxygen atoms. It occurs naturally in Earth's atmosphere as a trace gas. 

Best of luck your future