Exam Review- Fall 2021- Algebra I Day 1

• ​Classifying #s

• ​order of operations

• ​phrases to expressions

• ​properties

• ​expression values

• ​multistep equations

• ​absolute value equations

• ​literal equations

• ​inequalities

Translating Phrases

We use the word Equality when there is an = sign.

• 1 undo addition or subtraction

• 2 undo multiplication or division

• The exception ... a GIANT fraction!!

with review

Think of the absolute value equation as a variable when performing operations to get it isolated. Notice we add 10 to both sides then divide both sides by 3 to get |x-2| isolated. Now the problem |x-2| = 7 can be solved like we just learned.

• When graphing your inequality on the number line, the open circle means the number is not included.

• When graphing your inequality on the number line, the closed circle means the number is included.

Any measurement is always positive, including distance. you can't run a negative mile, even if you run it backwards, you still ran the mile.

You can remove those vertical lines by changing what is inside them to a positive value. Easy enough for constants(numbers) right? try it.

Just like solving for A in an equation, we can do the same for |A|. remember that the value inside the absolute value symbols is the distance from 0. So you can see A=5 if we travel 5 places to the right. Notice if we travel 5 places to the left, we arrive at -5. So A can equal both -5 or 5, depending on what direction we travel.

So when we solve for a, we see if a=5, then |5| also equals 5. We also see if a= -5 that |-5| = 5. We can see that when taking the absolute value of a variable, we will have 2 answers; the answer for moving right(towards positive numbers) and the answer for moving left(towards negative numbers).

If we want to solve this like the one before, would we say Y= 5 or -5??? Let us try and see.

y=5 then |5| = -5. That does not seem right, because |5| = 5 not -5. What about if y= -5 then |-5| = -5, that also is not right, because

|-5| = 5. So y has no solution because an absolute value can never equal a negative number. You try some.

We can apply this process to more advanced absolute value equations.

Notice that we have setup two equations. Both equations have the absolute value symbols removed. But one of them has the value switched to a negative. This is how we find out the distance, one going left and one going right from our starting point on a number line. We solve both equations by isolating the variable, just like we have done before. Both equations are solved by adding 5 to both sides. We have our two answers for X; X=7, X=3.

Think of the absolute value equation as a variable when performing operations to get it isolated. Notice we add 10 to both sides then divide both sides by 3 to get |x-2| isolated. Now the problem |x-2| = 7 can be solved like we just learned.

Since absolute value is always a positive number, we need to make sure that the equation makes since. Notice in the picture as we start isolating the absolute value part that we end up with |x+2| = -2/3.

Since an absolute value can not equal a negative number, there would be no solution. try some,

use paper and pencil as needed.