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checking answer for equation

Posted January 23rd, 2008 by Wesley892
in

Find x from this equation:
-2/3(6/5x-7/10)=17/20

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Comments

clarification

On January 23rd, 2008 Isoscel says:

Is it:

1)

$$-\frac{2}{3}(\frac{6}{5}x-\frac{7}{10})=\frac{17}{20}$$

or:

2)

$$-\frac{2}{3}(\frac{6}{5x}-\frac{7}{10})=\frac{17}{20}$$

?

The first equation.

On January 23rd, 2008 Wesley892 says:

The first equation.

Nice to have you

On January 24th, 2008 Structure says:

Nice to have you back!

$$-\frac{2}{3}(\frac{6}{5}x-\frac{7}{10})=\frac{17}{20}$$

First of all you can get rid of $ -\frac{2}{3} $ in front. How can you do it? Very simple by multiplying with its inverse $ -\frac{3}{2} $ both terms of the equation.

$$(-\frac{3}{2})(-\frac{2}{3})(\frac{6}{5}x-\frac{7}{10})=-\frac{3}{2}\frac{17}{20}$$

you get

$$\frac{6}{5}x-\frac{7}{10}=-\frac{51}{40}$$

Next you can add $ \frac{7}{10} $ to the both sides and have

$$\frac{7}{10}+\frac{6}{5}x-\frac{7}{10}=\frac{7}{10}-\frac{51}{40}$$

Now it rest

$$\frac{6}{5}x=\frac{28}{40}-\frac{51}{40}$$

or

$$\frac{6}{5}x=\frac{28-51}{40}=-\frac{23}{40}$$

You can finish getting rid of $ \frac{6}{5} $. How can you do it?
The same way you did it before, multiplying both sides by its inverse $ \frac{5}{6} $

$$\frac{5}{6}.\frac{6}{5}x=\frac{5}{6}(-\frac{23}{40})$$

You have

$$x=-\frac{23}{48}$$

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