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CalcGospel 國際數學圖譜

Equation Intersections Explorer

Rearrange an equation and see why its real solutions stay unchanged

中文辅助说明

把等式中的任意一项拖到等号另一边,观察左右两式对应的曲线怎样改变。移项相当于等式两边同时加上或减去同一个函数,因此两条曲线的交点高度可能改变,但交点的 x 坐标和实数解个数保持不变。手机上也可以先点选一项,再点击等号另一边。

Interactive demonstration

Move a term across the equals sign

Drag a term to the other side, or tap a term and then tap the opposite side. Its sign changes, but every solution guide remains fixed.

Current equation

The two sides become two curves

Choose any term
Left side · blue curve
Move selected term here
Right side · rose curve
Move selected term here

Graphical view

Same solution lines, different curves

Dashed vertical lines mark the x-coordinates of every intersection.