Multi-Step & Variables on Both Sides 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 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 on both the left and right sides, requiring manipulation to isolate the variable.

Front

How do you solve the equation 6x + 10 = 2(3x + 4)?

Back

First, distribute the 2: 6x + 10 = 6x + 8. Then, subtract 6x from both sides: 10 = 8, which is a contradiction, indicating no solutions.

Front

What is the solution to the equation -18 - 6x = 6(1 + 3x)?

Back

First, distribute the 6: -18 - 6x = 6 + 18x. Then, add 6x to both sides and combine like terms to find x = -1.

Front

How do you isolate the variable in the equation 14p - 8 = 22 + 20p?

Back

First, subtract 14p from both sides: -8 = 22 + 6p. Then, subtract 22 from both sides: -30 = 6p. Finally, divide by 6 to get p = -5.

Front

What is the solution to the equation 10x - 6x = 23 + 5?

Back

Combine like terms: 4x = 28. Then, divide by 4 to find x = 7.

Front

How do you solve the equation 2(x + 5) - 7 = 3(x - 2)?

Back

First, distribute: 2x + 10 - 7 = 3x - 6. Then, simplify to 2x + 3 = 3x - 6. Subtract 2x from both sides to find x = 9.

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 parenthesis.

Front

What does it mean if an equation has no solution?

Back

An equation has no solution when the variable cancels out and results in a false statement, indicating that there are no values that satisfy the equation.

Front

What does it mean if an equation has infinite solutions?

Back

An equation has infinite solutions when the variable cancels out and results in a true statement, indicating that any value for the variable will satisfy the equation.