Solving Multistep Equations with Special Solutions

Front

What is a multistep equation?

Back

A multistep 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 solutions?

Back

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

Front

What is the first step in solving the equation 11 - 3x = 44?

Back

Subtract 11 from both sides.

Front

Solve for x: 9x + 7 − 5x = 4x − 7

Back

No solutions.

Front

What is the solution to the equation f - 4 = 6f + 26?

Back

f = -6.

Front

Solve for x: 3x + 1 + 2x = 4x − 2 − 7x + 7

Back

x = ½.

Front

What is the solution to the equation 4x + 1 = 8x − 3?

Back

x = 1.

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 for an equation to have infinitely many solutions?

Back

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

Front

What is the process of combining like terms?

Back

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