Solving Linear Equations

Front

Is x = 6 a solution of the equation 24 = 2x + 12?

Back

Yes, substituting x = 6 gives 24 = 2(6) + 12, which simplifies to 24 = 24.

Front

Solve for v: 3v + 6 = 51

Back

v = 15.

Front

5(x - 3) + 6 = 5x - 9

Back

This equation is an Identity, meaning it is true for all values of x.

Front

Which operation will cancel out multiplication?

Back

Division.

Front

Which of the following equations would have no solution? 3(-2x+4)=-6x-12

Back

This equation has no solution because it simplifies to 0 = 0, which is always true.

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed, typically in the form y = mx + b.

Front

What does it mean for an equation to have one unique solution?

Back

It means there is exactly one value of the variable that satisfies the equation.

Front

What is the solution to the equation 2x + 3 = 11?

Back

x = 4.

Front

What is the definition of a contradiction in equations?

Back

A contradiction occurs when an equation simplifies to a false statement, such as 0 = 5.

Front

How do you isolate a variable in an equation?

Back

You perform inverse operations to get the variable alone on one side of the equation.