Solving Linear Equations

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. 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 2x + 5 = 12?

Back

Subtract 5 from both sides to isolate the term with the variable: 2x = 12 - 5.

Front

How do you isolate the variable in the equation 4x + 1 = 7x - 5?

Back

Rearrange the equation to get all terms with x on one side and constant terms on the other side: 4x - 7x = -5 - 1.

Front

What is the solution to the equation 8x + 2 + 3x + 5 = x + 12?

Back

Combine like terms to simplify: 11x + 7 = x + 12, then solve for x.

Front

What does it mean to combine like terms in an equation?

Back

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

Front

What is the solution to the equation 2 - 4x = 3x - 12?

Back

Rearranging gives: 2 + 12 = 4x + 3x, which simplifies to 14 = 7x, so x = 2.

Front

How do you check if your solution to a linear equation is correct?

Back

Substitute the value of the variable back into the original equation to see if both sides are equal.

Front

What is the distributive property in solving equations?

Back

The distributive property states that a(b + c) = ab + ac, allowing you to multiply a single term by each term inside a parenthesis.

Front

What is the solution to the equation 6(2x + 1) = 18?

Back

First, apply the distributive property: 12x + 6 = 18, then solve for x.