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 first step in solving the equation 3(x - 2) = 18?

Back

Distribute the 3 to both terms inside the parentheses: 3x - 6 = 18.

Front

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

Back

Subtract 4x from both sides to get 1 = 3x - 5, then add 5 to both sides to isolate the term with x.

Front

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

Back

The solution is x = 1.

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 makes the equation true, often resulting in a contradiction.

Front

What is the solution to the equation 2(2x + 3) = -6(x + 9)?

Back

The solution is x = -6.

Front

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

Back

Substitute the solution back into the original equation to see if both sides are equal.

Front

What is the solution to the equation 7x - 3x - 8 = 24?

Back

The solution is x = 8.

Front

What is the importance of combining like terms in solving linear equations?

Back

Combining like terms simplifies the equation, making it easier to isolate the variable.