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How many solutions does x+3+2x=3x+2 have

1 Answer

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Answer: No solutions

Work Shown

x+3+2x=3x+2

3x+3=3x+2

3x+3-3x = 3x+2-3x ....... subtract 3x from both sides

0x+3 = 0x+2

0+3 = 0+2

3 = 2

We end up with a false equation, so the original equation is always false regardless of what we pick for x.

The equation has no solutions

We consider the equation to be a contradiction. This is because the left and right sides reach different numbers (i.e. the sides do not agree on the same value).

If you were to graph y = x+3+2x and y = 3x+2, you should notice that those equations produce parallel lines that never intersect. This is a visual indicator of "no solutions".

User Miguelarc
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