Solving Equations with Variables on Both Sides

Front

What does it mean to solve an equation with variables on both sides?

Back

It means to find the value(s) of the variable(s) that make the equation true, where the variable appears on both sides of the equation.

Front

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

Back

The first step is to isolate the variable by moving all terms containing the variable to one side of the equation.

Front

What does it mean if an equation has 'no solution'?

Back

It means that there are no values for the variable that can satisfy the equation, often resulting in a contradiction.

Front

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

Back

It means that any real number can be a solution to the equation, indicating that the two sides of the equation are equivalent for all values.

Front

Solve: x + 2 = x + 4

Back

no solution

Front

What is the process to solve the equation 5y + 34 = -2(-7y + 1)?

Back

Distribute the -2, combine like terms, and isolate y to find the solution.

Front

Solve: 5y + 34 = -2(-7y + 1)

Back

y = 4

Front

What is the significance of combining like terms in an equation?

Back

Combining like terms simplifies the equation, making it easier to isolate the variable.

Front

Solve: 5x - 14 = 8x + 4

Back

x = -6

Front

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

Back

To isolate a variable means to manipulate the equation so that the variable is alone on one side, making it easier to solve.