M4 Solving Equations with variables on both sides

Front

What does it mean to have variables on both sides of an equation?

Back

It means that the variable (like x or f) appears on both sides of the equation, and you need to manipulate the equation to isolate the variable.

Front

How do you solve an equation with variables on both sides?

Back

You can solve it by moving all terms involving the variable to one side and constant terms to the other side, then simplifying.

Front

What is the first step in solving the equation 3(x - 1) = 2x + 9?

Back

Distribute the 3 on the left side to get 3x - 3 = 2x + 9.

Front

What is the solution to the equation 3(x - 1) = 2x + 9?

Back

x = 12.

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.

Front

What does it mean if an equation has infinite solutions?

Back

It means that any value for the variable will satisfy the equation, often resulting from equivalent expressions on both sides.

Front

Back

All real numbers.

Front

What is the solution to the equation 2(x + 6) + 3 = 9 + 5x?

Back

x = 2.

Front

How do you isolate a variable in an equation?

Back

You perform inverse operations to move other terms away from the variable.

Front

What is the solution to the equation f - 4 = 6f + 26?

Back

f = -6.