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 simplify an equation?

Back

To simplify an equation means to combine like terms and reduce it to its simplest form.

Front

What is the first step in solving the equation 10x + 2(x – 6) = 3(4x – 4)?

Back

Distribute the 2 on the left side and the 3 on the right side.

Front

How do you isolate the variable in an equation?

Back

To isolate the variable, perform inverse operations to get the variable by itself on one side of the equation.

Front

What is the solution to the equation 7x – 4 + x = -1 + 13x + 7?

Back

The solution is x = -2.

Front

What does it mean if an equation has infinitely many solutions?

Back

It means that any value for the variable will satisfy the equation.

Front

What is the purpose of checking your solution in an equation?

Back

To verify that the solution satisfies the original equation.

Front

What is a coefficient in a linear equation?

Back

A coefficient is a numerical factor that multiplies a variable in an equation.

Front

What is the difference between one solution and no solution in linear equations?

Back

One solution means there is a specific value for the variable that satisfies the equation, while no solution means there is no value that can satisfy the equation.

Front

What does it mean to combine like terms?

Back

Combining like terms means to add or subtract terms that have the same variable raised to the same power.