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# Solve: $|2x - 1| = |3x + 5|$. Write your answers as a list of numbers, separated by commas, e.g. '23, 19' (but without the quotes).

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Solve: $$|2x - 1| = |3x + 5|$$. Write your answers as a list of numbers, separated by commas, e.g. "23, 19" (but without the quotes).

Mar 22, 2019

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Solve:

$$|2x - 1| = |3x + 5|$$.

e.g. '23, 19' (but without the quotes).

$$\begin{array}{|rcll|} \hline |2x - 1| &=& |3x + 5| \\ (2x - 1)^2 &=& (3x + 5)^2 \\ 4x^2-4x+1&=& 9x^2+30x+25 \\ \ldots \\ 5x^2 +34x+24 &=& 0 \\\\ x &=& \dfrac{-34\pm \sqrt{34^2-4\cdot 5 \cdot 24} }{2\cdot 5} \\ &=& \dfrac{-34\pm \sqrt{34^2-480} }{10} \\ &=& \dfrac{-34\pm \sqrt{676} }{10} \\ &=& \dfrac{-34\pm 26 }{10} \\\\ x &=& \dfrac{-34+ 26 }{10} \\ \mathbf{x} & \mathbf{=} & \mathbf{-0.8}\\\\ x &=& \dfrac{-34- 26 }{10} \\ \mathbf{x} & \mathbf{=} & \mathbf{-6}\\ \hline \end{array}$$

$$\mathbf{"-0.8, -6"}$$

Mar 22, 2019