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 3(5x + 10) + 10 = 6x - (x + 10)?

Back

Distribute the 3 on the left side: 15x + 30 + 10 = 6x - x - 10.

Front

How do you isolate the variable x in an equation?

Back

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

Front

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

Back

The solution is x = 2.

Front

What is a flat fee in a pricing model?

Back

A flat fee is a fixed charge that does not change regardless of the amount of service provided.

Front

How do you set up an equation to compare two pricing models?

Back

Set the total costs of both models equal to each other and solve for the variable representing the hours.

Front

What is the solution to the equation 7x + 5 + x - 3 + x = 5?

Back

The solution is x = 1/3.

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

Back

The solution is x = -2.