Solving Multi-Step Equations

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 solve the equation 2(2x + 3) = -6(x + 9)?

Back

First, distribute both sides: 4x + 6 = -6x - 54. Then, combine like terms and isolate x to find x = -6.

Front

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

Back

An equation has no solution when the variables cancel out and you are left with a false statement, such as 0 = 5.

Front

What is the first step in solving multi-step equations?

Back

The first step is to distribute any terms that are multiplied by parentheses.

Front

What does it mean if an equation has 'infinite solutions'?

Back

An equation has infinite solutions when every value of the variable satisfies the equation, often resulting in a true statement like 0 = 0.

Front

How do you combine like terms in an equation?

Back

Combine like terms by adding or subtracting coefficients of the same variable or constant terms.

Front

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

Back

Isolating the variable allows you to solve for its value, making it easier to understand the relationship between the variables.

Front

What is the correct order of operations when solving multi-step equations?

Back

The correct order is: 1) Distribute, 2) Combine like terms, 3) Add or subtract to get the variable on one side, 4) Divide or multiply to solve for the variable.

Front

How do you solve the equation 7x + 19 = -2x + 55?

Back

First, combine like terms: 7x + 2x = 55 - 19. Then, solve for x to find x = 4.

Front

What is the significance of checking your solution in an equation?

Back

Checking your solution ensures that the value you found satisfies the original equation, confirming its correctness.