1. Heart of Algebra Lessons 1 & 2
Simplifying expressions and absolute value
Evaluating expressions and formulas
Writing expressions from sentences
Solve Equations
Literal Equations
Solve Inequalities
Absolute Value Equations and Inequalities

2. Simplifying expressions and absolute value
Remember to only add “like terms” which includes all variables and matching exponents
When multiplying a polynomial by a monomial remember to distribute
When dividing a polynomial by a monomial remember to divide each piece by the monomial. It may be helpful to rewrite.
Simplify inside the absolute value bars before applying the bars to the single number

3. Evaluating expressions and formulas
If you are allowed a calculator, remember that negative numbers should be typed in parentheses. Do not push the minus sign for a negative number!
When evaluating formulas be sure to chose the correct unit at the end of the problem
Area is units squared Ex) cm2
Volume is units cubed Ex) ft3
Rates are unit per unit Ex) miles per hour

4. Writing expressions from sentences
Know your key words
Addition: sum, increased by, more
Subtraction: difference, decreased by, less
Three less than a number means to take 3 away! n – 3
Multiplication: product, times, twice, triple
Division: quotient, divided by
Watch for needed parentheses!

5. Solving Equations Distribute and simplify each side
Move letters to one side (left) and move numbers to the other side (right)
Divide or multiply to get the letter alone
To move a fraction in front of the letter – multiply by the reciprocal
Remember to multiply by a fraction you multiply by the numerator and divide by the denominator

6. Literal Equations
To move an equation containing multiple letters around follow all the same rules of solving equations
Move pieces in addition and subtraction first
Move the pieces in multiplication or division last
These include solving formulas for a different variable

7. Solving Inequalities Solve inequalities just like you solve equations
If you multiply or divide BY a negative number for your last step remember to flip the inequality sign!
Less than sign looks like an L that is tipped <
Greater than sign does not look like an L >
When graphing solutions remember that < and > use open circles because the answer is not included where as ≤ and ≥ use closed circles because the answer is included

8. Absolute Value Equations and Inequalities
Absolute Value equations have two answers
Isolate the absolute value before writing the two new equations
1st equation as is – drop bars
2nd equation – drop bars and make right side negative
Solve absolute value inequalities like equations
Flip the inequality symbol when writing the 2nd problem
Less than problems make a single answer in the middle
Greater than problems make two answers on the ends of the graph