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There are many different kinds of equations, and each kind requires special techniques for solving; so it probably isn't possible to give rules that are valid in all cases. In any case, here are some specific examples; I am sure there are others which I don't remember right now:

Trigonometric equations quite often have an infinite number of solutions, because they are periodic. To give a simple example, sin x = 0 has the solution x = 0, but also pi, 2xpi, 3xpi, etc. (equivalent to 180 degrees, 360 degrees, etc.), because of the periodic nature of the sine function.

If a variable disappears when solving an equation, if you get a true statement the solution set is the set of all real numbers. For example, 2(x+1) = 2x + 2. Solving, you get: 2x + 2 = 2x + 2, or 0 = 0. Note that the variable "x" disappeared.

There are many different kinds of equations, and each kind requires special techniques for solving; so it probably isn't possible to give rules that are valid in all cases. In any case, here are some specific examples; I am sure there are others which I don't remember right now:

Trigonometric equations quite often have an infinite number of solutions, because they are periodic. To give a simple example, sin x = 0 has the solution x = 0, but also pi, 2xpi, 3xpi, etc. (equivalent to 180 degrees, 360 degrees, etc.), because of the periodic nature of the sine function.

If a variable disappears when solving an equation, if you get a true statement the solution set is the set of all real numbers. For example, 2(x+1) = 2x + 2. Solving, you get: 2x + 2 = 2x + 2, or 0 = 0. Note that the variable "x" disappeared.

There are many different kinds of equations, and each kind requires special techniques for solving; so it probably isn't possible to give rules that are valid in all cases. In any case, here are some specific examples; I am sure there are others which I don't remember right now:

Trigonometric equations quite often have an infinite number of solutions, because they are periodic. To give a simple example, sin x = 0 has the solution x = 0, but also pi, 2xpi, 3xpi, etc. (equivalent to 180 degrees, 360 degrees, etc.), because of the periodic nature of the sine function.

If a variable disappears when solving an equation, if you get a true statement the solution set is the set of all real numbers. For example, 2(x+1) = 2x + 2. Solving, you get: 2x + 2 = 2x + 2, or 0 = 0. Note that the variable "x" disappeared.

There are many different kinds of equations, and each kind requires special techniques for solving; so it probably isn't possible to give rules that are valid in all cases. In any case, here are some specific examples; I am sure there are others which I don't remember right now:

Trigonometric equations quite often have an infinite number of solutions, because they are periodic. To give a simple example, sin x = 0 has the solution x = 0, but also pi, 2xpi, 3xpi, etc. (equivalent to 180 degrees, 360 degrees, etc.), because of the periodic nature of the sine function.

If a variable disappears when solving an equation, if you get a true statement the solution set is the set of all real numbers. For example, 2(x+1) = 2x + 2. Solving, you get: 2x + 2 = 2x + 2, or 0 = 0. Note that the variable "x" disappeared.

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14y ago

There are many different kinds of equations, and each kind requires special techniques for solving; so it probably isn't possible to give rules that are valid in all cases. In any case, here are some specific examples; I am sure there are others which I don't remember right now:

Trigonometric equations quite often have an infinite number of solutions, because they are periodic. To give a simple example, sin x = 0 has the solution x = 0, but also pi, 2xpi, 3xpi, etc. (equivalent to 180 degrees, 360 degrees, etc.), because of the periodic nature of the sine function.

If a variable disappears when solving an equation, if you get a true statement the solution set is the set of all real numbers. For example, 2(x+1) = 2x + 2. Solving, you get: 2x + 2 = 2x + 2, or 0 = 0. Note that the variable "x" disappeared.

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Q: How can you find out if an equation has infinitely many solutions?
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