Special Cases for Equations

Front

Solve: 10x + 3 + 3x = 5x + 1 + 8x + 2

Back

x = -3, x = 3, infinitely many solutions, no solutions. Answer: infinitely many solutions.

Front

Solve: 9x + 7 − 5x = 4x − 7

Back

x = 7, x = -7, infinitely many solutions, no solutions. Answer: no solutions.

Front

Solve: 5x + 4 = 5x − 3

Back

x = 4, x = -3, infinitely many solutions, no solutions. Answer: no solutions.

Front

Solve: 2y − 3 = 2y − 3

Back

y = 0, y = -3, infinitely many solutions, no solutions. Answer: infinitely many solutions.

Front

Solve: 4x + 1 = 8x − 3

Back

x = 1, x = 2, infinitely many solutions, no solutions. Answer: x = 1.

Front

What does 'infinitely many solutions' mean in equations?

Back

It means that there are countless values of the variable that satisfy the equation.

Front

What does 'no solutions' mean in equations?

Back

It indicates that there are no values of the variable that can satisfy the equation.

Front

What is the first step in solving linear equations?

Back

Combine like terms on both sides of the equation.

Front

What is a linear equation?

Back

An equation that makes a straight line when graphed, typically in the form ax + b = c.

Front

What is the significance of isolating the variable in an equation?

Back

Isolating the variable helps to find its value by simplifying the equation.