Distribute, Combine like terms, and Solve

Front

What is the process of distributing in algebra?

Back

Distributing involves multiplying a term outside of parentheses by each term inside the parentheses. For example, in 3(2x + 4), you would calculate 3*2x + 3*4 = 6x + 12.

Front

How do you combine like terms?

Back

Combining like terms means adding or subtracting terms that have the same variable raised to the same power. For example, in the expression 2x + 3x, you combine them to get 5x.

Front

What does it mean to solve an equation?

Back

Solving an equation means finding the value of the variable that makes the equation true. For example, in the equation x + 3 = 7, solving gives x = 4.

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 parentheses.

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It has the form ax + b = c, where a, b, and c are constants.

Front

How do you isolate a variable in an equation?

Back

To isolate a variable, you perform inverse operations to get the variable alone on one side of the equation. For example, in x + 5 = 10, subtract 5 from both sides to get x = 5.

Front

What is the first step in solving the equation 43 = -3x - 4(-x - 9)?

Back

The first step is to distribute -4 to both terms inside the parentheses: -4 * -x = 4x and -4 * -9 = 36, resulting in 43 = -3x + 4x + 36.

Front

What is the solution to the equation 5x + 4(4x - 21) = -84?

Back

First, distribute 4 to get 5x + 16x - 84 = -84. Combine like terms to get 21x - 84 = -84, then add 84 to both sides to find 21x = 0, so x = 0.

Front

How do you solve the equation -7x + 2(6x + 16) = 57?

Back

Distribute 2 to get -7x + 12x + 32 = 57. Combine like terms to get 5x + 32 = 57, then subtract 32 from both sides to find 5x = 25, so x = 5.

Front

What is the solution to the equation -7x + 6(5x - 6) = 240?

Back

Distribute 6 to get -7x + 30x - 36 = 240. Combine like terms to get 23x - 36 = 240, then add 36 to both sides to find 23x = 276, so x = 12.