How To Solve an Algebraic Expression

1. How To Solve an Algebraic Expression Step by Step Instructions

2. The Algebraic Expression An algebraic expression is a mathematical expression where you have one or more unknown variables – like “x” or “y”. An expression can involve any mathematical processes, and may have more than one. Since it is an expression, there is no “equals” symbol. Usually, an expression gives a value for “x” or “y” and asks that you evaluate or “solve”. Here is an example of an algebraic expression…. 4(x-2) + 3x + x2

3. First Things First…. The first thing we want to do is simplify the expression. When we simplify, it just means we are getting the expression into the simplest form. That means you solve until you cannot solve any further. Three of the most important steps to simplifying are: • Resolving anything you see in parentheses • Combining like terms • Solving to lowest point

4. Parentheses In an algebraic expression, parentheses are used to separate parts of an expression. Look at our equation… 4(x-2) + 3x + x2 To get rid of these parentheses, we have to use the distributive property. That means we will multiply the number on the outside with each part of the expression inside the brackets. Here is how it looks…. 4x-8 + 3x + x2

5. Combining Like Terms Our next step is to combine like terms. When we combine like terms, we take anything that is the same and put them together. Remember our expression? Our like terms are in green…. 4x - 8 + 3x + x2 When we put like terms together, it looks like this…. 4x+3x - 8+ x2 Always remember, when you combine like terms, be sure to move the symbol immediately in front of the term with it!They always move together!

6. Simplify When we have all our like terms together, simplify as much as you can. Our expression simplified looks like this…. 7x- 8+ x2 You know your expression is in simplest form when you have nothing else you can add, subtract, multiply or divide!

7. Evaluate Now that we have gotten our expression into the simplest form, we need to evaluate it. When you evaluate, you are solving the expression with a number in place of the “x”. 7x - 8+ x2 Let’s say that in our expression, x = 2. We replace every “x” in our expression with a “2”. The new equation looks like this…. 7(2)- 8+ (2)2

8. Order of Operations Now that everything in our expression is a number, we need to solve. When we solve, we use The Order of Operations. • Parentheses - Solve any calculations in parentheses • Exponents - Simplify any exponents • Multiplication / Division – Working from left to right • Addition / Subtraction - Working from left to right 14 – 8 + 4 And the answer is…. 10

9. Putting It All Together Hopefully, you have learned each possible part of an algebraic expression and how to solve them. Try and solve these five expressions: 1. 6y2-15 - y; if y = 3 • 6y2- 15 – y • 6(3)2 – 15 – 3 • 6(9) – 15 – 3 • 54 – 15 – 3 • 36

10. Let’s Practice!!! 2. 2(x-5) + 3x; if x = 3 • 2x – 10 + 3x • 2x + 3x - 10 • 5x - 10 • 5(3) -10 • 15 – 10 • 5

11. Let’s Practice!!! 3. 4y – 3y2 + 1 – 2y2; if y = 1 • 4y – 3y2 + 1 – 2y2 • -3y2 – 2y2 + 4y + 1 • -5y2+ 4y + 1 • -5(1)2 + 4(1) + 1 • -5 + 4 + 1 • 0

12. Let’s Practice!!! 4. x – 3y ; if x = 9 and y = (-2) • 9 – 3(-2) • 9 + 6 • 15

13. Let’s Practice!!! 5. a2 + 8a + 1; if a = 2 • a2 + 8a + 1 • 22 + 8(2) + 1 • 4 + 16 + 1 • 21

14. Congratulations!!! Well done! You have learned how to solve an algebraic expression!

15. Created and Presented By: Noah Childress 8th Grade Mrs. Eller