Multi Step Equations (one, many, no solution)

Front

What is a multi-step equation?

Back

A multi-step equation is an equation that requires more than one step to solve, often involving operations such as addition, subtraction, multiplication, and division.

Front

How do you isolate a variable in a multi-step equation?

Back

To isolate a variable, perform inverse operations to move all terms involving the variable to one side of the equation and constant terms to the other side.

Front

What does it mean if an equation has no solution?

Back

An equation has no solution if there are no values for the variable that make the equation true, often resulting in a contradiction.

Front

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

Back

The first step is to distribute the 2 to both terms inside the parentheses: 3x + 8x - 8 = 3.

Front

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

Back

The solution is x = 1.

Front

What is a contradiction in the context of equations?

Back

A contradiction occurs when simplifying an equation leads to a false statement, such as 0 = 5, indicating no solution exists.

Front

What is the significance of the equation 3(2x+1) = 6x+1 having no solution?

Back

This indicates that the left side and right side of the equation are equivalent for all values of x, leading to a false statement when simplified.

Front

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

Back

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

Front

What is the result of simplifying the expression 5 - 2(x - 7)?

Back

The result is 5 - 2x + 14, which simplifies to 19 - 2x.

Front

What does it mean to solve for x in an equation?

Back

To solve for x means to find the value of x that makes the equation true.