Solving Equations Variables on Both Sides

Front

What is the solution to the equation x - 2x + 3 = 3 - x?

Back

All real numbers.

Front

Solve for x: 5x - 14 = 8x + 4.

Back

x = -6.

Front

What is the solution to the equation 6(5g + 2) = 30g?

Back

No solution.

Front

Solve for a: 1 + 9a - 8 = 8a.

Back

a = 7.

Front

What is the solution to the equation 5(2x - 1) = -5 + 10x?

Back

All real numbers.

Front

Define 'variable' in the context of equations.

Back

A symbol used to represent an unknown value.

Front

What does it mean to isolate a variable in an equation?

Back

To manipulate the equation so that the variable is on one side and all other terms are on the other.

Front

What is the principle of balancing equations?

Back

Whatever you do to one side of the equation, you must do to the other side to maintain equality.

Front

Explain the concept of 'no solution' in equations.

Back

It means that there are no values for the variable that will satisfy the equation.

Front

What does it mean if an equation has 'all real numbers' as a solution?

Back

Any real number can be substituted for the variable, and the equation will hold true.