How do you solve #\frac { 5x } { 6} + \frac { 3x } { 10} = - 2#?

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Answer 1 · 2018-04-28T17:16:49

#(5x)/6 + (3x)/10 = -2#

To solve for #x#, you need a common denominator

#(25x)/30 + (9x)/30 = - 60/30#

#(34x)/30 = -60/30# (reduce fractions)

#(17x)/15 = -30/15# (Cross multiply and isolate x)

#x = -30/17#

the need is to isolate x and create a balanced equation.
create a common denominator , add the fractions then cross multiply.

#x = (-30*15) / (17*15)#

the #15#s cancel #15/15=1# thus left with

#x= -30/17#

Answer 2 · 2018-04-28T17:30:25

#x = -30/17#

When you have fractions in an equation, you can get rid of them right at the start.

Multiply each term by the LCD, which in this case is #30# so that the denominators can cancel.

#(5x)/6+(3x)/10 = -2#

#(color(blue)(cancel30^5xx5x))/cancel6+(color(blue)(cancel30^3xx3x))/cancel10 = -2color(blue)(xx30)#

#25x+9x = -60#

#34x =-60#

#x = -60/34#

#x = -30/17#