Solving equations with variables on both sides

Front

What is an equation with variables on both sides?

Back

An equation that contains variables on both the left and right sides, requiring manipulation to isolate the variable.

Front

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

Back

1. Simplify both sides of the equation. 2. Move all variable terms to one side and constant terms to the other. 3. Isolate the variable.

Front

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

Back

To manipulate the equation so that the variable is alone on one side, making it easy to determine its value.

Front

What is the first step in solving the equation 2(4x - 3) - 8 = 4 + 2x?

Back

Distribute the 2 on the left side: 8x - 6 - 8 = 4 + 2x.

Front

What is the solution to the equation 8x - 8 = -4x + 16?

Back

x = 2.

Front

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

Back

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

Front

What does the term 'distributive property' refer to?

Back

A property that states a(b + c) = ab + ac, used to eliminate parentheses in equations.

Front

How do you check if your solution to an equation is correct?

Back

Substitute the solution back into the original equation to see if both sides are equal.

Front

What is the solution to the equation 12x - 15 = 3(2x + 3)?

Back

x = 4.

Front

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

Back

y = 4.