How do you solve #-3/11=(5-h)/(h+1.4)#?

First, multiply each side of the equation by #color(red)(11)color(blue)((h + 1.4))# to eliminate the fractions while keeping the equation balanced. #color(red)(11)color(blue)((h + 1.4))# is the Lowest Common Denominator of the two fractions:

#color(red)(11)color(blue)((h + 1.4)) xx -3/11 = color(red)(11)color(blue)((h + 1.4)) xx(5 - h)/(h + 14.4)#

#cancel(color(red)(11))color(blue)((h + 1.4)) xx -3/color(red)(cancel(color(black)(11))) = color(red)(11)cancel(color(blue)((h + 1.4))) xx(5 - h)/color(blue)(cancel(color(black)(h + 14.4)))#

#color(blue)((h + 1.4))(-3) = color(red)(11)(5 - h)#

Next, expand the terms in parenthesis on both sides of the equation by multiplying each term within the parenthesis by the term outside the parethesis:

#(-3 xx color(blue)(h)) + (-3 xx color(blue)(1.4)) = (color(red)(11) xx 5) - (color(red)(11) xxh)#

#-3h - 4.2 = 55 - 11h#

Then, add #color(red)(4.2)# and #color(blue)(11h)# to each side of the equation to isolate the #h# term while keeping the equation balanced:

#-3h - 4.2 + color(red)(4.2) + color(blue)(11h) = 55 - 11h + color(red)(4.2) + color(blue)(11h)#

#-3h + color(blue)(11h) - 4.2 + color(red)(4.2) = 55 + color(red)(4.2) - 11h + color(blue)(11h)#

#(-3 + color(blue)(11))h - 0 = 59.2 - 0#

#8h = 59.2#

Now, divide each side of the equation by #color(red)(8)# to solve for #h# while keeping the equation balanced:

#(8h)/color(red)(8) = 59.2/color(red)(8)#

#(color(red)(cancel(color(black)(8)))h)/cancel(color(red)(8)) = 7.4#

#h = 7.4#

#-3/11=(5-h)/(h+1.4)#

#:.-3/11=(5-h)/(h+14/10)#

multiply L.H.S. and R.H.S. by # (h+14/10)#

#:.-3/11(h+14/10)=5-h#

#:.-3/11h-(14/10)(3/11)=5-h#

#:.-3/11h-42/110=5-h#

#:.-3/11h+h=5+42/110#

#:.-3/11h+11/11h=5+42/110#

#:.8/11h=5 42/110#

#:.8/11h=592/110#

:.#(80h=592)/110#

multiply L.H.S. and R.H.S. by #110#

#:.80h=592#

#:.h=592/80#

#:.color(purple)(h=7.4#

check:

substitute #color(purple)(h=7.4#

#:.-3/11=(5-7.4)/(7.4+1.4)#

#:.-3/11=-2.4/8.8#

#:.-3/11=-0.272727272#

#:.color(purple)(-0.272727272=-0.272727272#