Algebra Case

Chapter 3 Essay

Callie Doren

Period: 6

In chapter three, section 1, we learned about graphing and writing inequalities. The symbols we are going to use a lot are <-less than,>- greater than ≤-less than or equal to, ≥-greater than or equal to. You may be asking how would I graph these inequalities, well you have to make sure it comes down to a variable and one of those symbols with a number after it. Like, this example would be x<5. To determine whether it's open or closed is when if it's greater than or equal to or less than or equal too, or the greater & less than sign with a line under it. If it's a normal sign you would leave the circle you have to put on the graph open. If it's not you color it in, and which direction it should go, well you probably don't know, but I'm here to tell you. To determine which direction to point your arrow on the graph you have to draw on every problem would be whatever way your symbol is pointing. Remember the variable has to be on the left side.

In chapter three, section 2, we learned how to solve these inequalities with addition and subtraction. Solving one step inequalities is much like solving one step equations. To solve an Inequality, you need to isolate the variable using the properties of inequality and inverse operations. For addition, you can add the same number to both sides of an inequality, and the statement will still be true. Now for subtraction, you can subtract the same number from both sides of an inequality and the statement will still be true. So whether it's subtraction or addition it will always be true. A helpful hint would be to use an inverse operation to "undo" the operation in an inequality. If the inequality contains addition, use subtraction to undo the addition. Objectives in this section would be to learn how to solve one step inequalities by using addition, and to learn how to solve one step inequalities by using subtraction. An example would be, x+9<15, since nine is added to x, you would subtract 9 from both sides to undo the addition. After that you would end up with x+0<6, you need to get x by itself so +0 means nothing and you would cross that out and your ending answer would be x<6. To graph this on a number line it would look like the graph above.

In chapter 3, section 3, we learned about solving inequalities with multiplication and division. * When multiplying or dividing by a negative you must flip the inequality. Remember, solving inequalities is similar to solving equations. To solve an inequality that contains multiplication or division, undo the operation by multiplying or dividing both sides of the inequality by the same number. The objectives for this section are to be able to solve one step inequalities by using multiplication, and learning to solve