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How Do You Solve an Equation with No Solution?
Solve the following problem: 10 + 6x = 15 + 9x – 3x
Summary
- 'x' is the variable that we're trying to solve for
- To make progress with this equation, we start by simplifying the 9x-3x on the right side
- To finish up, we need to bring all of the 'x' terms on one side
- No need to keep solving, because we got something crazy! 10 DOES NOT EQUAL 15!!

Notes
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- If you look on the right side of the equation, you can combine like terms to simplify the problem.
- To subtract 3x from 9x, just remember that 9-3=6, and so if you had 9 x's and you took away 3 of them, you'd have 6 x's left:)
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- You want to get all of the variables on the same side!
- Subtract 6x from both sides.
- Since you have 6x on both sides of the equation, it cancels out on both sides, resulting in 10=15, which is obviously NOT TRUE!
- This equation has no solution because no matter what value you assign to x, the answer will never be true!