Linear equations are equations for a straight line end to end (even though they go on forever). There are many different ways to write them, but when we go to interpret them you should have the y-variable isolated on the left-hand side of the equation. The y-variable can be undergoing an operation, but you need sure to remove and exponents for it to be valid. This is really the first time that we start to balance equations.

We use inequality as a sentence using symbol other than the sign = (equals). The symbols >, ≤ , >, and ≥ are most common inequality. For solving inequality sentences, you will follow the same method that you would use if it were an equation with the following exception. The direction of the inequality will change, if you multiply or divide both side with a -ve value. Then, we will this variation a negative multiplication property of inequality. If a, b, and c are real numbers and c has -ve value, the conditions of variables will be a < b, then, ac > bc or if a > b, then the variables ac < bc. Example : Solve for x: 3 x - 7 > 20. Step 1: 3x -7 > 20 -> (1) Step 2: 3x > 27 Step 3: x > 9. To verify the solution, you will observe either x = 9 making the equation (1) true or not. Even though 9 is not a solution, it is a crucial value or point of division that is vital to explore the solution. 3x - 7 = 20 Step 1: 3(9) - 7 = 20 Step 2: 27 - 7 = 20. Then, we will select the value greater than 9 to 10. Observe whether it makes the actual inequality true or not. 3x - 7 > 20 Step 1: 3(10) - 7 > 20 Step 2: 30 - 7 > 20 Step 3: 23 > 20. It is true sentence. It is difficult to write all greater than 9 numbers together so we will use set builder notation. { x| x > 9} These worksheets explain how to balance equations that contain linear inequalities. We suggest that you have colored pencils handy to help shade the graphs.