How do you solve #-2- \frac{3}{4} b = - \frac{11}{16}#?

2 Answers
Mar 15, 2017

#-2-\frac{3}{4}\cdotb=-\frac{11}{16}#

#-\frac{3}{4}\cdotb=-\frac{11}{16}+2#

#-\frac{3}{4}\cdotb=\frac{-11+32}{16}#

#-\frac{3}{4}\cdotb=\frac{21}{16}#

#b=\frac{21}{16}\cdot(-\frac{4}{3})#

#b=-\frac{7}{4}#

#b=-21/12=-7/4#

Explanation:

#"Note "3/4b=(3b)/4#

To eliminate the fractions in the equation multiply ALL terms on both sides by the #color(blue)"lowest common multiple"# ( LCM) of the denominators 4 and 16

The LCM of 4 and 16 is 16

#(16xx-2)-(cancel(16)^4xx(3b)/cancel(4)^1)=(cancel(16)^1xx-11/cancel(16)^1)#

#rArr-32-12b=-11larrcolor(red)" no fractions"#

add 32 to both sides.

#cancel(-32)cancel(+32)-12b=-11+32#

#rArr-12b=21#

divide both sides by - 12

#(cancel(-12) b)/cancel(-12)=21/(-12)#

#rArrb=-21/12=-7/4#

#color(blue)"As a check"#

Substitute this value into the left side of the equation and if equal to the right side then it is the solution.

#-2-(3/4xx-21/12)=-2+21/16=-11/16#

#rArrb=-21/12=-7/4" is the solution"#