1. Write an equation for “3 more than twice a is 24.”

1. Bellwork 1. Write an equation for “3 more than twice a is 24.” 2. A square has a side length of 8 feet. Find the area of the square using the formula A=s2. 3. A rectangular serving tray is 26 inches long by 18 inches wide. What is the tray’s serving area? • Subtraction Property • Subtracting the same number to each side of an equation produces an equivalent equation • If x+a=b, then x+a-a=b-a, or x=b-a

2. Bellwork Solution 1. Write an equation for “3 more than twice a is 24.” • Subtraction Property • Subtracting the same number to each side of an equation produces an equivalent equation • If x+a=b, then x+a-a=b-a, or x=b-a

3. Bellwork Solution 2. A square has a side length of 8 feet. Find the area of the square using the formula A=s2. • Subtraction Property • Subtracting the same number to each side of an equation produces an equivalent equation • If x+a=b, then x+a-a=b-a, or x=b-a

4. Bellwork Solution 3. A rectangular serving tray is 26 inches long by 18 inches wide. What is the tray’s serving area? • Subtraction Property • Subtracting the same number to each side of an equation produces an equivalent equation • If x+a=b, then x+a-a=b-a, or x=b-a

5. Rewrite Equations and Formulas Section 3.8

6. The Concept • Today we’re going to take a step back and look at the equation solving process with variables • Functionally this is done no different than with numbers

7. Addition and Subtraction Property (review) • Addition Property • Adding the same number to each side of an equation produces an equivalent equation • If x-a=b, then x-a+a=b+a, or x=b+a • Subtraction Property • Subtracting the same number to each side of an equation produces an equivalent equation • If x+a=b, then x+a-a=b-a, or x=b-a

8. Multiplication & Division Property (review) • Multiplication Property • Multiplying each side of an equation by the same nonzero number produces an equivalent equation • Division Property • Dividing each side of an equation by the same non-zero number produces an equivalent equation

9. Steps for Solving an Equation • Simplify Equation • Expand Equations • Combine Like Terms • Collect variable terms on one side of the equation • Use properties of equalities • Combine new like terms • Solve for our variable • Opposite Order of Operations • Addition/Subtraction • Multiplication/Division • Exponents • Parenthesis • Check your Solution

10. Vocabulary • Let’s take a look at a new definition • Literal Equation • An equation where all coefficients and constants have been replaced by letters • e.g. 2x+1=5 transformed into the literal equation, ax+b=c

11. Usefulness of Literary Equations • Why are these important? • When an equation is a literal one it can be used to symbolize any number of equations based on the multitude of values that each letter can symbolize i.e. it becomes a formula • For instance, when 2x+1=5 is transformed into the literal equation, ax+b=c, it can be applied for any equation given that there are numerical values to input into a, b, and c. • We can also use literal equations much like a real equation to solve for the various variables contained within, thus creating useful formulas

12. Examples Let’s start by solving this equation for y Can we take it a step further?

13. Another important tool This is we’re we’ll begin to use the process of reverse distribution as well.

14. Steps for Solving an Equation • Simplify Equation • Expand Equations • Combine Like Terms • Collect variable terms on one side of the equation • Use properties of equalities • Combine new like terms • Solve for our variable • Opposite Order of Operations • Addition/Subtraction • Multiplication/Division • Exponents • Parenthesis • Check your Solution

15. Steps for Solving an Equation Important Reminders We can do whatever we want to an equation as long as we do it to both sides Group your variable terms on one side and then combine like terms or perform reverse distribution

16. Practice Let’s plug in A=64.4 and b=4 to find h

17. Homework • 3.8 • 1-10, 11-19 odd, 20-25, 32-35, 38-45

18. Practical Example • Writing equations • Example 6, Page 186 • It’s helpful for us to rewrite equations, especially if we’re going to be using them a lot. • Solve our temperature formula for F so that we can find F when C=14 and 10 degrees Celsius

19. Practical Example The Great Pyramid of Giza is located in the city of Giza, which today is part of Greater Cairo, Egypt. The initial height of the pyramid was 145.75 meters, but it has lost 10 meters off its top. It ranked as the tallest structure on Earth until the nineteenth century. It consists of approximately 2 million blocks of stone, each weighing over two tons. The base of the pyramid measures 229 meters on each side. Use the formula S = b2 + 2bh where b is the base and h is the height, to find the surface area of the pyramid at its original height.

20. Practical Example • The Second Pyramid of Gizah in Egypt has a Surface Area of 108453.7125m2 and a base of 215.25m. What is its height?

21. Most Important Points • Definition of a literal equation—an equation where the constants and coefficients have been replaced by variables • To rewrite an equation for a variable we simply utilize or processes and properties of equalities