No Solution/Infinite Solution/One Solution

Front

What does it mean if an equation has no solution?

Back

An equation has no solution when there are no values for the variable that can satisfy the equation. This often occurs when the two sides of the equation represent parallel lines that never intersect.

Front

What does it mean if an equation has infinitely many solutions?

Back

An equation has infinitely many solutions when any value for the variable satisfies the equation. This typically happens when the equation simplifies to a true statement, such as 0=0.

Front

What does it mean if an equation has one solution?

Back

An equation has one solution when there is exactly one value for the variable that satisfies the equation. This occurs when the two sides of the equation represent lines that intersect at a single point.

Front

Solve for x: 4x - 9 = 3.5x - 9

Back

x = 0

Front

Solve for x: -2(x + 1) = x - 3x - 2

Back

Infinite solutions

Front

Solve for x: x + 6 = x

Back

No solution

Front

What is the solution to the equation 0 = 0?

Back

Infinite solutions

Front

Solve for x: 6x - 18 = 4(2x - 3) - (2x + 6)

Back

Infinite solutions

Front

What is the first step in solving the equation 4x - 9 = 3.5x - 9?

Back

Isolate the variable by moving all terms involving x to one side.

Front

What is the significance of parallel lines in relation to solutions of equations?

Back

Parallel lines indicate that the equations have no solution because they never intersect.