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Essential Question: How do you solve equations with variables? Before we start… Which of the following would be considered an equation? 3x 7 16 4 x 4 What is an equation? A mathematical sentence formed by placing an equal sign, =, between two expressions. 𝑥 + 8 = 12 What is a solution? A number that produces a true statement when it is substituted for the variable. How do you write verbal sentences as equations? • To write a verbal sentence as an equation you will translate words into operations and mathematical symbols. • The word is represents an equal sign. Write as equations. The sum of x and 6 is 9. The difference of 12 and y is 15. Write as equations. The product of −4 and p is 32. The quotient of n and 2 is 9. Write as equations. The sum of 3 and z is −10. The quotient of m and 6 is 4. Write as equations. The difference of x and 8 is −4. The sum of 26 and y is 43. The quotient of p and 7 is 16. The product of 14 and m is 56. How do you check to see if a number is a solution? • You substitute the number in for the variable and see if it produces a true statement. Tell whether 9 or 7 is a solution of x 5 2 x Tell whether 52 or 60 is a solution of 13 4 Tell whether 6 or 3 is a solution of x 9 12 Tell whether 13 or 9 is a solution of 91 7c What about solving equations? • Solving the equation is finding all solutions of an equation. • You can use mental math to solve a simple equation by thinking of the equation as a question. How can you solve equations with variables? • Some equations can be solved by using mental math. Using Mental Math • Some equations are simple enough to solve using mental math. • Think of the equation as a question. • Once you answer the question, check the solution. 4. x 10 7 5. 2 n 6 6. 3w 15 36 7. 4 s From 1998 to 2002, biologist Jane Shen-Miller grew several lotus plants from ancient seeds she found in China. The oldest seed was about 500 years old. Estimate the year when this seed was formed. Go-cart rides cost $5 each at a county fair. During the first day of the fair, the go-cart operator takes in a total of $1000. How many times did people ride the go-carts that day? Write and solve an equation to find the answer. The dragonfly is the fastest flying insect. It can move at a speed of 50 feet per second. Find the approximate time it takes a dragonfly to travel 400 feet. Write and solve an equation. You divide a bag of trail mix into 8 portions for you and your friends to have as snacks on a bike ride. Each portion weighs 3 ounces. Find the total weight of the trail mix originally in the bag. Write and solve an equation. How do you solve equations with variables? Ticket Out the Door Solve the equation using mental math. 7 x 63