Equations w/ Variables on Both Sides(Fractions, Distributive

Front

What is the distributive property in algebra?

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

How do you isolate a variable in an equation?

Back

To isolate a variable, you perform inverse operations to both sides of the equation until the variable is alone on one side.

Front

What does it mean to have variables on both sides of an equation?

Back

Having variables on both sides means that the variable appears in expressions on both the left and right sides of the equation, requiring manipulation to solve for the variable.

Front

What is the first step in solving an equation with variables on both sides?

Back

The first step is to simplify both sides of the equation, if necessary, and then move all terms containing the variable to one side.

Front

How do you solve the equation 4(1 - x) + 3x = -2(x + 1)?

Back

Distribute the 4 and -2, combine like terms, and isolate x to find x = -6.

Front

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

Back

The solution is y = 4.

Front

How do you simplify the equation 4(2x - 1) = 6x + 5 - 5x + 5?

Back

Distribute the 4, combine like terms on both sides, and solve for x to find x = 2.

Front

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

Back

The solution is p = -5.

Front

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

Back

Rearrange the equation to isolate x, leading to the solution x = -6.

Front

What is the importance of checking your solution in an equation?

Back

Checking your solution ensures that the value satisfies the original equation, confirming its correctness.