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

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Answer 1 · 2018-06-14T00:58:20

#y=-15/8#

Let's take a look at the denominators first. We have

#5, 2# and #4#. What is the GCF (Greatest Common Factor) of these? Let's just multiply the two highest numbers to get

#20#, which is our GCF. We can multiply this by every term to get rid of the fractions, so let's do that!

#20(-2/5)y-20(1/2)=20(1/4)#

This simplifies to

#(-40/5)y-20/2=20/4#

Which further simplifies to

#-8y-10=5#

Now, we can deal with this easily by adding #10# to both sides to get

#-8y=15#

Our last step would be to divide both sides by #-8# to solve for #y#. We get

#color(blue)(y=-15/8)#

All I did was multiply every term by a number that was a multiple of all three denominators to get whole numbers.

From that point on, this was a straightforward linear equation we solved by isolating the variable.

Hope this helps!