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 x - 5 = 7?

Back

Add 5 to both sides of the equation to isolate x.

Front

What is the solution to the equation 5x = -35?

Back

x = -7, found by dividing both sides by 5.

Front

How do you isolate the variable in the equation 2 - 4x = 3x - 12?

Back

Combine like terms and move all terms involving x to one side of the equation.

Front

What is the solution to the equation 7 - 5x = 12?

Back

x = -1, found by isolating x on one side.

Front

What is the purpose of checking your solution in a linear equation?

Back

To verify that the value found for the variable satisfies the original equation.

Front

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

Back

x = 4, found by rearranging the equation to isolate x.

Front

What does 'combining like terms' mean in the context of solving equations?

Back

It means to simplify the equation by adding or subtracting terms that have the same variable.

Front

What is the importance of maintaining balance when solving equations?

Back

Maintaining balance means performing the same operation on both sides of the equation to keep it true.