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 6(2x + 1) = 18?

Back

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

Front

How do you isolate the variable in the equation 7x - 3x - 8 = 24?

Back

Combine like terms (7x - 3x = 4x) to get 4x - 8 = 24, then add 8 to both sides to isolate the term with x.

Front

What is the solution to the equation 5 + 3x = 8x - 15?

Back

The solution is x = 4.

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

Front

What is the solution to the equation 4x + 1 = 7x - 5?

Back

The solution is x = 2.

Front

What is the purpose of using inverse operations when solving equations?

Back

Inverse operations are used to undo operations in order to isolate the variable and solve the equation.