How do you solve #\frac { 2x + 5} { 5} - \frac { x + 2} { 4} = - 1#?

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Answer 1 · 2017-11-01T10:54:50

LCM
#(2x +5 xx 4 - x +2 xx 5)/20=-1#

#(8x+20-5x+10)/20=-1#
#(3x+30)/20=-1#
#3x+30=-20#
#3x=-50#
#x=-50/3#
OR,
#x=-16.bar(6666)#
Or,
#x=16 2/3#

Answer 2 · 2017-11-01T11:31:42

#color(magenta)(x=-10#

#(2x+5)/5-(x+2)/4=-1#

multiply both sides by 20

#:.cancel20^4xx(2x+5)/cancel5^1-cancel20^5xx(x+2)/cancel4^1=20xx-1#

#:.4(2x+5)-5(x+2)=-20#

#:.8x+20-5x-10=-20#

#:.3x+20-10+20=30#

#:.3x+30=0#

#:.3x=-30#

#:.color(magenta)(x=-10#

~~~~~~~~~~~~~~~~~~~~

check:-

substitute# color(magenta)(x=-10#

#(2(color(magenta)(-10))+5)/5-((color(magenta)(-10))+2)/4=-1#

#:.(-20+5)/5-(-8/4)=-1#

#:.-15/5+8/4=-1#

#:.-3+2=-1#

#:.color(magenta)(-1=-1#