Solving 1-Variable Equations (Special Cases)

Front

What is a one-variable equation?

Back

An equation that contains only one variable, such as x or y, and can be solved to find the value of that variable.

Front

What does it mean if an equation has no solution?

Back

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

Front

What does it mean if an equation has infinitely many solutions?

Back

It means that there are countless values for the variable that can satisfy the equation, often occurring when both sides of the equation are equivalent.

Front

Solve the equation: 4 − 6x − 2 = −2(3x − 1)

Back

infinitely many solutions

Front

Solve the equation: 3x + 1 + 2x = 4x − 2 − 7x + 7

Back

x = ½

Front

What is the first step in solving a one-variable equation?

Back

Combine like terms on both sides of the equation.

Front

Solve the equation: 9y − 5 = 2y + 9

Back

y = 2

Front

What is the purpose of isolating the variable in an equation?

Back

To find the value of the variable that makes the equation true.

Front

Solve the equation: 3(x − 1) = 2x + 9

Back

x = 12

Front

What is the distributive property?

Back

A property that states a(b + c) = ab + ac, used to simplify expressions.