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

Front

What does it mean when an equation has no solution?

Back

An equation has no solution when there is no value for the variable that makes the equation true. This often occurs when simplifying leads to a false statement, such as 0 = 5.

Front

What is the first step in solving the equation 2x + 1 = 5x - 3?

Back

The first step is to get all terms involving x on one side and constant terms on the other side, typically by subtracting 2x from both sides.

Front

How do you solve the equation 4 + k/2 = -3 for k?

Back

Subtract 4 from both sides to get k/2 = -7, then multiply both sides by 2 to find k = -14.

Front

What is the solution to the equation 3x - x + 2 = 4(2x - 1)?

Back

First, simplify the left side to 2x + 2. Then, distribute on the right side to get 8x - 4. Set 2x + 2 = 8x - 4 and solve for x, which gives x = 1.

Front

What is the solution to the equation 5x + 4 = -6?

Back

Subtract 4 from both sides to get 5x = -10, then divide by 5 to find x = -2.

Front

How do you solve the equation ½ (2x + 6) = 3x + 13?

Back

First, multiply both sides by 2 to eliminate the fraction, giving 2x + 6 = 6x + 26. Then, isolate x to find x = -5.

Front

What is the distributive property?

Back

The distributive property states that a(b + c) = ab + ac. It allows 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 infinite solutions?

Back

An equation has infinite solutions when any value for the variable satisfies the equation, often resulting from simplifying to a true statement like 0 = 0.

Front

What is a variable in an equation?

Back

A variable is a symbol, often represented by a letter, that stands for an unknown value in an equation.