An equation with no solution means that it is impossible for two expressions to equal each other.
Simplify 10 + 6x = 15 + 9x - 3x:
[tex]9x - 3x = 6x[/tex]
[tex]10 + 6x = 15 + 6x[/tex]
Subtract 6x from both sides:
[tex]10 = 15[/tex]
This equation has no solution.
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Simplify 11 + 3x = 6x + 5 - 3x:
[tex]6x - 3x = 3x[/tex]
[tex]11 + 3x = 3x + 5[/tex]
Subtract 3x from both sides:
[tex]11 = 5[/tex]
This equation has no solution.
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Simplify 6x - (3x + 8) = 16x:
[tex]6x - (3x + 8) = 6x - 3x - 8 = 3x - 8[/tex]
[tex]3x - 8 = 16x[/tex]
Subtract 3x from both sides:
[tex]-8 = 19x[/tex]
This equation has a solution, as x would equal -8/19.
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Simplify 6x - 2 - 3x = 3x - 2:
[tex]6x - 2 - 3x = 3x - 2[/tex]
[tex]3x - 2 = 3x - 2[/tex]
This equation has infinite solutions, as both expressions are the same.
