Multi-Step Equations with Variables on Both Sides

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 operations such as addition, subtraction, multiplication, and division.

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 of the equation, requiring manipulation to isolate the variable.

Front

How do you isolate a variable in a multi-step equation?

Back

To isolate a variable, you perform inverse operations to move all terms containing the variable to one side of the equation and constant terms to the other side.

Front

What is the first step in solving the equation 4(2a + 3) = -3(a - 1) + 31?

Back

The first step is to distribute the numbers outside the parentheses: 8a + 12 = -3a + 3 + 31.

Front

What is the importance of combining like terms in an equation?

Back

Combining like terms simplifies the equation, making it easier to isolate the variable and solve.

Front

How do you check your solution after solving an equation?

Back

To check your solution, substitute the value back into the original equation to see if both sides are equal.

Front

What is the solution to the equation 5y + 34 = -2(-7y + 1)?

Back

The solution is y = 4.

Front

What does it mean to have a negative coefficient in front of a variable?

Back

A negative coefficient indicates that the variable's value will decrease when multiplied by that coefficient.

Front

How do you handle fractions when solving equations?

Back

You can eliminate fractions by multiplying both sides of the equation by the least common denominator.

Front

What is the solution to the equation -8x - 8 + 3(x - 2) = -3x + 2?

Back

The solution is x = -8.