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

2 Answers
David Drayer
Jun 23, 2017

x = 0

Explanation:

Multiply all the terms by 15 the least common multiple.

# 15 xx -( 2x -6)/3 = 15 xx( x/5 + 2)# This gives

# -10x + 30 = 3x + 30# subtract 30 from both sides

# -10x + 30 - 30 = 3x + 30 - 30 # the result is

# - 10 x = 3x # add 10x to both sides

# -10x + 10x = 3x + 10x # which equals

# 0 = 13 x # divide both sides by 13

# 0/13 = (13x)/13 # the answer is

# 0 = x #

Y
Jun 23, 2017

Answer: #x=0#

Explanation:

Solve #-(2x-6)/3=x/5+2# for #x#.

We can start by getting rid of the fractions by multiplying everything by the least common multiple (lcm) of the denominators (#3#, #5#, and #1#), which is #15#.

So, we get:
#15(-(2x-6)/3=x/5+2)#

#-5(2x-6)=3x+30#

Simplifying, we get:
#-10x+30=3x+30#

Subtracting #30# from both sides and adding #10x# to both sides, we get:
#13x=0#

Dividing both sides by #13#, we get our answer:
#x=0#

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