How Many Solutions?

Front

What does it mean if an equation has infinite solutions?

Back

Any value for x will make the equation true.

Front

What does it mean if an equation has one solution?

Back

There is exactly one value of x that satisfies the equation.

Front

What does it mean if an equation has no solution?

Back

There is no value of x that can satisfy the equation.

Front

Solve for x: 8 - 4x = -4x + 8

Back

Infinite solutions.

Front

Solve for x: 3x + 1 = 12x - 1

Back

One solution.

Front

Solve for x: 2(3x - 1) - (-5 - x) = 7x + 3

Back

Infinite solutions.

Front

Solve for x: 3w + 1 = 12w + 1

Back

One solution.

Front

What is the first step in solving the equation 3x + 1 = 12x - 1?

Back

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

Front

What is the significance of like terms in an equation?

Back

Like terms can be combined to simplify the equation.

Front

What is the process of checking a solution in an equation?

Back

Substituting the solution back into the original equation to verify if both sides are equal.