Solving Equations with Special Cases

Front

Solve the equation: 10x - 9 = 2x + 63. State if it has one, many, or no solutions.

Back

x = 9, one solution.

Front

Solve the equation: 4(r + 2) - 3 = 4r - 11. State if it has one, many, or no solutions.

Back

No solution.

Front

For the equation 3(10x + 5) = 30x + n, which value of n will create an equation with infinitely many solutions?

Back

n = 15.

Front

Solve the equation: 3(2x - 8) = 2(3x - 12). State if it has one, many, or no solutions.

Back

Many solutions.

Front

Solve the equation: 11x - 5 = 8x + 31. State if it has one, many, or no solutions.

Back

x = 12, one solution.

Front

What is a linear equation?

Back

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

Front

What does it mean if an equation has no solution?

Back

It means there is no value for the variable that can satisfy the equation.

Front

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

Back

It means that any value for the variable will satisfy the equation.

Front

What is the first step in solving a linear equation?

Back

Isolate the variable on one side of the equation.

Front

What is the significance of the coefficients in a linear equation?

Back

Coefficients determine the slope and position of the line when graphed.