Multi-Step Equations Error Analysis

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

What does it mean if an equation has 'no solution'?

Back

An equation has 'no solution' if there are no values that can satisfy the equation, often resulting in a contradiction.

Front

What is an identity in terms of equations?

Back

An identity is an equation that is true for all values of the variable, meaning both sides of the equation are always equal.

Front

How do you determine if a solution to an equation is correct?

Back

To determine if a solution is correct, substitute the solution back into the original equation and check if both sides are equal.

Front

What is the first step in solving a multi-step equation?

Back

The first step is often to simplify both sides of the equation, which may include combining like terms or distributing.

Front

What does it mean to combine like terms?

Back

Combining like terms involves adding or subtracting terms that have the same variable raised to the same power.

Front

How do you isolate a variable in an equation?

Back

To isolate a variable, perform inverse operations to get the variable alone on one side of the equation.

Front

What is the distributive property?

Back

The distributive property states that a(b + c) = ab + ac, allowing you to multiply a single term by each term inside a parenthesis.

Front

What is the cost to paint a wall that is 12 feet long and 23 feet wide if paint costs $0.08 per square foot?

Back

The area of the wall is 12 * 23 = 276 square feet. The cost is 276 * $0.08 = $22.08.

Front

What is the solution to the equation 5d = 2d - 18?

Back

The solution is d = -6, after isolating d by adding 2d to both sides and then dividing by 3.