24-25 Solving Multi-step Equations/Literal/Applications

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 combining like terms, using the distributive property, and isolating the variable.

Front

What does it mean if an equation has no solution?

Back

An equation has no solution when there is no value for the variable that makes the equation true, often resulting in a contradiction.

Front

What does it mean if an equation has infinite solutions?

Back

An equation has infinite solutions when any value for the variable satisfies the equation, often resulting in an identity.

Front

How do you solve the equation 8z - 22 = 3(3z + 11) - z?

Back

First, simplify the right side: 8z - 22 = 9z + 33 - z. Then combine like terms: 8z - 22 = 8z + 33. This leads to -22 = 33, which is a contradiction, so there is no solution.

Front

What is the first step in solving the equation 0.4x + 1.6 = -1.6x + 53.2?

Back

The first step is to combine like terms by adding 1.6x to both sides: 0.4x + 1.6x + 1.6 = 53.2.

Front

What is the solution to the equation ax - b = c + d?

Back

The solution is x = (c + b + d) / a.

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 two or more terms inside a set of parentheses.

Front

What does it mean to isolate a variable?

Back

Isolating a variable means rearranging an equation so that the variable is on one side and all other terms are on the opposite side.

Front

What is a contradiction in an equation?

Back

A contradiction occurs when the equation simplifies to a false statement, indicating that there is no solution.

Front

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

Back

To check your solution, substitute the value back into the original equation to see if both sides are equal.