one solution, no solution, infinite solutions

Front

What is meant by 'one solution' in a linear equation?

Back

A linear equation has 'one solution' when there is exactly one value of the variable that satisfies the equation.

Front

What does 'no solution' mean in the context of linear equations?

Back

'No solution' occurs when the equations represent parallel lines that never intersect, meaning there is no value for the variable that can satisfy both equations.

Front

What does 'infinite solutions' mean in a linear equation?

Back

'Infinite solutions' occur when the equations represent the same line, meaning any value of the variable will satisfy the equation.

Front

Solve for x: 2x + 3 = 7

Back

x = 2

Front

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

Back

x = 5

Front

Solve for x: 5x - 10 = 0

Back

x = 2

Front

What is the first step in solving the equation 4x + 8 = 24?

Back

Subtract 8 from both sides to isolate the term with x.

Front

What is the solution to the equation 2(x + 3) = 2x + 6?

Back

Infinite solutions, as both sides are equivalent.

Front

How do you determine if an equation has no solution?

Back

If simplifying the equation leads to a false statement, such as 0 = 5, it has no solution.

Front

What is the solution to the equation 6x - 18 = 4(2x - 3) - (2x + 6)?

Back

Infinite Solution.