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Mathematics

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1. 2/(2/3)+3/4/(4/5)=
A. 1/5
B. 11/15
C. 47/60
D. 3 13/30
E. 12

2. If 2/5 of (2/3)/(5/6) is divided by 3/10, what is the resulting value?
A. 1/15
B. 12/25
C. 8/15
D. 5/3
E. 125/27

3. Solve for x: 2x+3<=11
Are there two answers?
4. Solve for x: 3x+4>=5x-8
Are there two answers?

  • Mathematics -

    1.

    2 / ( 2 / 3 ) = ( 2 / 1 ) / ( 2 / 3 ) =

    2 * 3 / ( 1 * 2 ) = 6 / 2 = 3


    ( 3 / 4 ) / ( 4 / 5 ) = 3 * 5 / ( 4 * 4 ) = 15 / 16

    2 / ( 2 / 3 ) + ( 3 / 4 ) / ( 4 / 5 = 3 + 15 / 16 = 3 15 / 16


    2.

    ( 2 / 3 ) / ( 5 / 6 ) = 2 * 6 / ( 3 * 5 ) = 12 / 15 = 3 * 4 / ( 3 * 5 ) = 4 / 5

    2 / 5 of ( 2 / 3 ) / ( 5 / 6 ) =

    ( 2 / 5 ) * ( 4 / 5 ) =

    2 * 4 / ( 5 * 5 ) = 8 / 25

    ( 8 / 25 ) / ( 3 / 10 ) = 8 * 10 / ( 3 * 25 ) =

    8 * 2 * 5 / ( 3 * 5 * 5 ) =

    8 * 2 / ( 3 * 5 ) =

    16 / 15 = ( 15 + 1 )/ 15 =

    15 / 15 + 1 / 15 = 1 1 / 15


    3.

    2 x < = 8 Subtract 3 to toth sides

    2 x + 3 - 3 < = 11 - 3

    2 x < = 8 Divide both sides by 2

    2 x / 2 < = 8 / 2

    x < = 4


    4.

    3 x + 4 > = 5 x - 8 Subtract 3 x to both sides

    3 x + 4 - 3 x > = 5 x - 8 - 3 x

    4 > = 2 x - 8 Add 8 to both sides

    4 + 8 > = 2 x - 8 + 8

    12 > = 2 x Divide both sides by 2

    12 / 2 > = 2 x / 2

    6 > = x

    That is same x < = 6

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