MATHEMATICS

Question

solve for x in each of the following 

 

a) 7^x=343

 

b) 2^-3=1/512

 

c) 2x-5/3=5/6

 

d) x+ 2 1/2=5 2/3

 

e) 20+x/x =4/5

 

f) 2x+4 = 3x - 1/3

 

Answer 1

a.  seven cubed is343

 

b. take reciprocals; i.e. 2 cubed = 512  BUT THIS IS NOT TRUE (did you omit an x somewhere??)

 

c.  multiply the entire equation by 6; this is CLEARING FRACTIONS and now you can solve by simple algebra skills.

 

d. convert the mixed numbers to improper fractions; then clear fractions (multiplying ALL terms by 6, the LCD. he rest will be easy.

 

e. this is defective; perhaps you must write it as (20+x)x.  As it is now, it says 21 = 4/5, which is FALSE. (THIS IS A PEMDAS PROBLEM, when parentheses are missing.)

Answer 2

a) 7^x=343

    7^x=7^3

        x=3

 

b) 2^(-x)=1/512 (I'm assuming this is what you mean !)

    1/2^x=1/(2^9)

    2^x=2^9

        x=9

 

c) 2x-5/3=5/6

    2x=5/6+5/3

    2x=5/6+10/6

    2x=15/6

    (1/2)(2x)=(1/2)(15/6)

     x=15/12

     x=5/4

     x=1 1/4

 

d) x+2 1/2=5 2/3

    x=5 2/3 - 2 1/2

    x=5 4/6 - 2 3/6

    x=3 1/6

 

e) ???

 

f) 2x+4=3x-1/3

   4+ 1/3=3x-2x

   x= 4 1/3