Solving Linear Equations

Front

What is a linear equation?

Back

A linear equation is an equation of the first degree, meaning it has no exponents greater than one. It can be written in the form ax + b = c, where a, b, and c are constants.

Front

What does it mean to solve a linear equation?

Back

To solve a linear equation means to find the value of the variable (usually x) that makes the equation true.

Front

What is the first step in solving the equation 7x + 5 + x - 3 + x = 5?

Back

Combine like terms: 7x + x + x = 9x and 5 - 3 = 2, so the equation becomes 9x + 2 = 5.

Front

How do you isolate the variable in the equation 9x + 2 = 5?

Back

Subtract 2 from both sides to get 9x = 3, then divide both sides by 9 to find x = 1/3.

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 a set of parentheses.

Front

How do you apply the distributive property to the equation 6(2x + 1) = 18?

Back

Distribute 6 to both terms inside the parentheses: 12x + 6 = 18.

Front

What is the next step after applying the distributive property in 12x + 6 = 18?

Back

Subtract 6 from both sides to get 12x = 12.

Front

How do you solve for x in the equation 12x = 12?

Back

Divide both sides by 12 to find x = 1.

Front

What does it mean to combine like terms?

Back

Combining like terms means to add or subtract terms that have the same variable raised to the same power.

Front

How do you combine like terms in the equation 8x + 2 + 3x + 5 = x + 12?

Back

Combine 8x and 3x to get 11x, and combine 2 and 5 to get 7, resulting in 11x + 7 = x + 12.