(7 question) Multistep Equations - Variables on Both Sides

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 to have variables on both sides of an equation?

Back

Having variables on both sides of an equation means that the variable appears in more than one term across the equal sign, requiring manipulation to isolate the variable.

Front

How do you solve the equation 3(x - 1) = 2x + 9?

Back

Distribute to get 3x - 3 = 2x + 9. Then, subtract 2x from both sides: x - 3 = 9. Finally, add 3 to both sides to find x = 12.

Front

What is the solution to the equation 4(2x + 1) = 5x + 3x + 9?

Back

Combine like terms to get 8x + 4 = 8x + 9. Subtract 8x from both sides to get 4 = 9, which is a contradiction. Therefore, there is no solution.

Front

What does it mean if an equation has infinite solutions?

Back

An equation has infinite solutions if every value of the variable satisfies the equation, often resulting from equivalent expressions on both sides.

Front

How do you solve the equation 12 + 2x - x = 9x + 6?

Back

Combine like terms to get 12 + x = 9x + 6. Subtract x from both sides: 12 = 8x + 6. Then, subtract 6 from both sides: 6 = 8x. Finally, divide by 8 to find x = \frac{3}{4}.

Front

What is the solution to the equation -2(x + 1) = -2x + 5?

Back

Distributing gives -2x - 2 = -2x + 5. Adding 2x to both sides results in -2 = 5, which is a contradiction. Therefore, there is no solution.

Front

How do you solve the equation 2(x + 2) + 3x = 2(x + 1) + 1?

Back

Distributing gives 2x + 4 + 3x = 2x + 2 + 1. Combine like terms to get 5x + 4 = 2x + 3. Subtract 2x from both sides: 3x + 4 = 3. Then, subtract 4 from both sides: 3x = -1. Finally, divide by 3 to find x = -\frac{1}{3}.

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 are like terms?

Back

Like terms are terms that have the same variable raised to the same power, allowing them to be combined through addition or subtraction.