Solve MultiStep 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 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. This often occurs when simplifying leads to a false statement, such as 0 = 5.

Front

How do you simplify the expression 5x + 3 - 2x + 1?

Back

Combine like terms: 5x - 2x + 3 + 1 = 3x + 4.

Front

What is the first step in solving the equation 3x - 8 = 3(x - 4) + 1?

Back

Distribute the 3 on the right side: 3x - 8 = 3x - 12 + 1.

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. This occurs when both sides of the equation are equivalent after simplification.

Front

How do you solve the equation 5x - 14 = 8x + 4?

Back

Rearrange to isolate x: 5x - 8x = 4 + 14, which simplifies to -3x = 18, so x = -6.

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 each term inside a parentheses.

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

Back

First, distribute: 3x + 8x - 8 = 3. Combine like terms: 11x - 8 = 3. Then, add 8 to both sides: 11x = 11, so x = 1.

Front

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

Back

Rearranging gives: f - 6f = 26 + 4, which simplifies to -5f = 30, so f = -6.