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\begin{array}{rlr} \sqrt{2 x+3}+\sqrt{x-2} & =4 & \\ \sqrt{2 x+3} & =4-\sqrt{x-2} \qquad \qquad \text { Subtract } \sqrt{x-2} \text { from both sides. } \\ (\sqrt{2 x+3})^{2} & =(4-\sqrt{x-2})^{2} \qquad \quad \text { Square both sides. } \end{array}