A linear equation has exactly one solution if solving it results in a specific value for the variable. Example: The equation 7x – 35 = 0 has one solution, x = 5.
An equation with no solution results in a false statement after solving, meaning there is no value that satisfies the equation. Example: The equation 7x – 35 = 5x + 2x – 27 has no solution because it simplifies to -35 = -27, which is false.
If an equation simplifies to a true statement regardless of the variable’s value, it has infinite solutions. Example: The equation 25x – 35 = 5(5x + 4) – 55 has infinite solutions because it simplifies to -35 = -35.
Practice Problems
Solve the following to determine if they have one solution, no solution, or infinite solutions: – 17x – 75 = 6 + 14x – 3x – 105 = 4(x – 20) – 1(x + 5)
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