2/3x +4=2x
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To your question: First bring all terms containing x to one side and constants to other side.
(3/2)(2/3x) + (3/2)(4)= (3/2)(2x)
Delta = (- 3)² - 4 * 2 * (- 4) = 9 + 32 = 41 x1 = (3 - sqr (41)) / 4 x2 = (3 + sqr (41)) / 4 <=> 2x² - 3x - 4 = 2 * (x - ((3 + sqr (41)) / 4)) * (x - (3 - sqr (41)) / 4)) <=> 2x² - 3x - 4 = 2 * 1/4 * 1/4 * (4x - 3 - sqr (41)) * (4x - 3 + sqr (41)) <=> 2x² - 3x - 4 = 1/8 * (4x - 3 - sqr (41)) * (4x - 3 + sqr (41)) roots are irrational because sqr (41) is irrationa
Is the question that complicated?
no
\[4 = 2x - 2/3x \] \[4 = 6/3x - 2/3x\] \[4 = 4/3 x\] \[4*3 = 4/3x *3\] \[12 = 4x\]\[12/4 = 4x / 4\]
Final Answer: x = 3
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\[\frac{2}{3}x+4=2x\] maybe multiply by 3 and get \[2x+12=6x\] subtract \(2x\) to get \(12=4x\) divide by \(4\) and get \(3=x\)
alternatively, start with \[\frac{2}{3}x+4=2x\] subtract \(\frac{2}{3}x\) from both sides and get \[4=\frac{4}{3}x\] then multiply both sides by \(\frac{3}{4}\) and get \[4\times \frac{3}{4}=x\] or \(x=3\)
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