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 of the variable that makes both sides of the equation equal.

Front

What is the first step in solving the equation 6x - 4 = 2(3x - 2)?

Back

Distribute the 2 on the right side: 6x - 4 = 6x - 4.

Front

What does IMS stand for in the context of equations?

Back

IMS stands for 'Infinitely Many Solutions', indicating that the equation is true for all values of the variable.

Front

How do you isolate the variable in the equation 5x - 7 = -10x + 8?

Back

Add 10x to both sides and then add 7 to both sides to isolate x.

Front

What is the solution to the equation 7y + 3 = 4y - 18?

Back

y = -7.

Front

What does 'No Solution' mean in the context of an equation?

Back

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

Front

How do you solve the equation - (6x + 7) = -6x + 8?

Back

Simplify both sides: -6x - 7 = -6x + 8, which leads to a contradiction.

Front

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

Back

x = -1.

Front

What is the importance of checking your solution in an equation?

Back

To verify that the value found satisfies the original equation.

Front

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

Back

It involves adding or subtracting terms that have the same variable and exponent.