Answer: no solution
3x - 2 = 3x -5
3x - 3x - 2 = 3x - 3x - 5 (Subtract 3x from each side.)
-2 = -5 Huh??
When you are solving an equation, and the variable disappears, there are two possibilities:
If you are left with a true statement (such as 2 = 2), then the equation is an identity, and any value of x will satisfy the equation. The number of solutions is infinite.
If you are left with a false statement, as in this case, no value of x will satisfy the equation. There is no solution.
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x=-.25.
3x2 = 21 describes two single values, and does not have an x intercept. 3x2 = 21 ∴ x2 = 7 ∴ x = ±√7
3x2-9x = 0 x(3x-9) = 0 x = 0 or x = 3
3x2 + 2x = 16 ∴ 3x2 + 2x - 16 = 0 ∴ 3x2 - 6x + 8x - 16 = 0 ∴ 3x(x - 2) + 8(x - 2) = 0 ∴ (3x + 8)(x - 2) = 0 ∴ x ∈ {-8/3, 2}
3x2 + x - 2 = 0(3x - 2) (x + 1) = 0x = + 2/3x = -1