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 that makes the equation true.

Front

What is the solution to the equation 2x + 3 = 11?

Back

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 a set of parentheses.

Front

How do you combine like terms in an equation?

Back

You combine like terms by adding or subtracting the coefficients of terms that have the same variable raised to the same power.

Front

What is the first step in solving the equation 3(x + 4) = 21?

Back

Distribute 3 to both terms inside the parentheses: 3x + 12 = 21.

Front

What does it mean if an equation has no solution?

Back

An equation has no solution if there is no value for the variable that can make the equation true, often resulting in a contradiction.

Front

What is the solution to the equation 5x - 2 = 3x + 6?

Back

x = 4

Front

What is an example of an equation with infinitely many solutions?

Back

An example is 2(x + 1) = 2x + 2, which simplifies to 2 = 2.

Front

What is the error in the equation 2x + 3 = 2x + 5?

Back

The error is that it leads to a false statement (3 = 5), indicating no solution.