Solving Funky Equations Examples

If we solve an equation and get 6 = 10 in the very last step, is the answer all real numbers or no solution?

There are two different funky answers we can get when solving an equation. When the values are exactly the same, such as 4 = 4 or x = x, the answer is all real numbers.

When the values are not equal, like 5 = 9 or -3 = 16, the answer is no solution.

The answer to this equation is no solution.

Solve for x in the following equation:

4x + 10 = 2(2x + 5)

One step at a time, y'all. Distribute the 2.

4x + 10 = 4x + 10

Subtract 4x.

4x + 10 – 4x = 4x + 10 – 4x

10 = 10

Since 10 always equals 10, this equation is true for all real numbers.

Solve for x in the following equation:

3x + 2 = 3x – 8

Subtract 3x from both sides to kick off this algebra party.

3x + 2 – 3x = 3x – 8 – 3x

2 = -8

Uh, 2 can't equal -8 (at least not in this dimension) so the solution is… no solution.