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

Front

How do you solve the equation 7x = 3x + 24?

Back

To solve for x, first subtract 3x from both sides: 7x - 3x = 24, which simplifies to 4x = 24. Then, divide both sides by 4: x = 6.

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 can satisfy the equation. This often occurs when simplifying leads to a false statement, such as 0 = 5.

Front

What is the goal of solving multi-step equations?

Back

The goal of solving multi-step equations is to find the value of the variable.

Front

How do you solve the equation 5x - 4 + 2x = 3?

Back

Combine like terms: 7x - 4 = 3. Then add 4 to both sides: 7x = 7. Finally, divide by 7: x = 1.

Front

What is the solution to the equation 14p - 8 = 22 + 20p?

Back

To solve for p, first rearrange the equation: 14p - 20p = 22 + 8. This simplifies to -6p = 30. Then divide by -6: p = -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 are like terms?

Back

Like terms are terms that have the same variable raised to the same power. For example, 3x and 5x are like terms, while 3x and 4y are not.

Front

How do you isolate a variable in an equation?

Back

To isolate a variable, you perform inverse operations to get the variable by itself on one side of the equation.

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. Subtract 2x from both sides: 1 = 3x - 3.