Variables on Both Sides: Number of Solutions

Front

What is a variable in an equation?

Back

A symbol that represents an unknown value in mathematical expressions or equations.

Front

What does it mean to have 'one solution' in an equation?

Back

It means there is exactly one value for the variable that makes the equation true.

Front

What does it mean to have 'no solution' in an equation?

Back

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

Front

What does it mean to have 'infinite solutions' in an equation?

Back

It means that any value for the variable will satisfy the equation, indicating that the two sides are equivalent.

Front

Solve for x: 5x - 2 = 7x + 8

Back

x = -5.

Front

Solve for x: 8x - 5 = 9x + 10

Back

x = -15.

Front

Solve for x: 6x - 4x + 10 = 2(x + 5)

Back

Infinite solutions.

Front

Solve for x: 3x - 7 = 3x + 8

Back

No solution.

Front

Solve for x: 5 - 7x = -7x + 9

Back

No solution.

Front

What is the first step in solving an equation with variables on both sides?

Back

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