Mathematics
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OpenStudy (anonymous):
solve for x!
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OpenStudy (anonymous):
\[\frac{ 1 }{ 2 }+\frac{ 4 }{ 2x}= \frac{ x+4 }{ 10 }\]
OpenStudy (solomonzelman):
multiply the 1st fraction (top and bottom) by x, add everything on the left side and cross multiply.
OpenStudy (anonymous):
how exactly do you do that?
OpenStudy (solomonzelman):
\[\frac{1}{2}+\frac{4}{2x}=\frac{x+4}{10}\]\[\frac{1 \times x}{2 \times x}+\frac{4}{2x}=\frac{x+4}{10}\]\[\frac{x}{2x}+\frac{4}{2x}=\frac{x+4}{10}\]\[\frac{x+4}{2x}=\frac{x+4}{10}\]\[2x=10\]\[x=5\]
OpenStudy (solomonzelman):
This should be helpful.
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OpenStudy (anonymous):
thanks. how about this one?
solve for x :\[\frac{ 2 }{ 5}+ \frac{ 3 }{ 5x}= \frac{ x+5 }{ 10 }\]
OpenStudy (anonymous):
@SolomonZelman
OpenStudy (solomonzelman):
\[\frac{2}{5}+\frac{3}{5x}=\frac{x+5}{10}\]
OpenStudy (solomonzelman):
\[\frac{2 \times x}{5 \times x}+\frac{3}{5x}=\frac{x+5}{10}\]
OpenStudy (solomonzelman):
\[\frac{2x}{5x}+\frac{3}{5x}=\frac{x+5}{10}\]
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OpenStudy (solomonzelman):
\[\frac{2x+3}{5x}=\frac{x+5}{10}\]
OpenStudy (solomonzelman):
\[\frac{2x+3}{x}=\frac{x+5}{2}\]
OpenStudy (solomonzelman):
\[4x+6=x^2+5x\]
OpenStudy (solomonzelman):
\[x^2+x-6=0\]
OpenStudy (solomonzelman):
\[(x+3)(x-2)=0\]
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OpenStudy (solomonzelman):
\[x=-3,~~~2\]
OpenStudy (anonymous):
so you basically factor it?
OpenStudy (solomonzelman):
when it is \[x^2+x-6=0\]after cross multiplying, yes!
OpenStudy (anonymous):
ha! i think i get it! ok ill just post and let you check my answers so you don't have to do all that again
OpenStudy (anonymous):
\[\frac{ 5 }{x^2-4 } + \frac{ 2 }{ x }+\frac{ 2 }{ x-2}\]
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OpenStudy (anonymous):
i got x = 8. is that right?
OpenStudy (anonymous):
@SolomonZelman
OpenStudy (solomonzelman):
retype the question please, (with the equal sign)
OpenStudy (anonymous):
oh whoops. just replace the last plus with equal
OpenStudy (solomonzelman):
\[\frac{5}{x^2-4}+\frac{2}{x}=\frac{2}{x-2}\]
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OpenStudy (solomonzelman):
\[\frac{2}{x}=\frac{2}{x-2}-\frac{5}{x^2-4}\]
OpenStudy (solomonzelman):
\[\frac{2}{x}=\frac{2}{x-2}-\frac{5}{(x+2)(x-2)}\]\[\frac{2}{x}=\frac{2(x+2)}{(x-2)(x+2)}-\frac{5}{(x+2)(x-2)}\]
OpenStudy (solomonzelman):
\[\frac{2}{x}=\frac{2(x+2)+5}{(x+2)(x-2)}\]\[\frac{2}{x}=\frac{2x+7}{(x+2)(x-2)}\]
OpenStudy (solomonzelman):
\[2x^2+7x=2x^2-8\]\[x=-7/8\]
OpenStudy (anonymous):
2 more?
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OpenStudy (anonymous):
\[\frac{ 2 }{ x +2 }+\frac{ 1 }{ 5 } = \frac{ 6 }{ x + 5}\]