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 2(3x + 4) + 2 = 4 + 3x?

Back

Distribute the 2 on the left side: 6x + 8 + 2 = 4 + 3x.

Front

How do you isolate the variable x 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 get 6 = 3x, and finally divide by 3 to find x = 2.

Front

What is the solution to the equation 10 = 3x - 12?

Back

The solution is x = 22/3.

Front

What is the process to solve the equation 12 = 20x - 18?

Back

Add 18 to both sides to get 30 = 20x, then divide by 20 to find x = 1.5 or x = 2.

Front

What does it mean to check your solution in a linear equation?

Back

Checking your solution means substituting the value of x back into the original equation to verify that both sides are equal.

Front

What is the solution to the equation 7 - 2(10x + 1) = 25?

Back

The solution is x = -1.

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.

Front

What is the definition of a coefficient in a linear equation?

Back

A coefficient is a numerical factor that multiplies a variable in an equation, such as the 3 in 3x.