Solving Two-Step Equations

Today’s Learning Goal We will continue to use our understanding of inverse operations to help us solve equations symbolically.

What does an inverse operation do? Consider the following situation: You ride your bike north for 4 miles and decide that you need to return to where you started. What do you need to do to get back to where you started? That’s right…ride your bike south 4 miles. This is similar to solving the equation x + 4 = 11. Because 4 was added to x to get 11, what needs to be done to undo adding 4 to determine the value of the unknown? Correct…subtract 4. x + 4 = 11 – 4 x=7

Another concrete example of inverse operations When you were getting ready for school this morning, most of you (still half asleep) put on your socks and then your shoes. If you decided that you wanted to change your shoes and socks, what would you have to do to get back to bare feet? Yes…take your shoes off first and then your socks. In this example, the order in which actions were done affected the order in which they were undone.

Inverse Operations Like the socks and shoes example, the order in which you undo the actions matters when dealing with numbers. Nice…4x – 3 = 21 For example, suppose you take an unknown number, you multiply it by 4, and then you subtract 3 from the total and you get 21. What is the equation you can write for this statement?

Solving a Two-Step Equation Given the equation below, what would we need to do first to try to determine the unknown number? 4x – 3 = 21 Great…we need to add three first because that was the last thing to be done (shoes then socks) x=24 Now we have an equation that looks like one we know how to solve. What would we do second to solve for the unknown number? Beautiful…divide both sides by 4. 44 44 x=6 Don’t forget you can check your answer! 4(6) – 3 = 21 It works!

Another Example What would be the equation for the following? Take a number and multiply it by -3. Then add 6 to the result to get x + 6 = 42 – 6 -3x=36  -3 x=-12 -3(-12) + 6 = 42 It works! What would you need to do first to undo what was done to the unknown number? Fantastic…subtract 6 from both sides. What do we do now to solve for x? Awesome…divide both sides by -3.

Solving Problems Using Equations The following is a table of values for Alana’s pledge plan including a $5 up-front fee plus $.50 per mile. What is the equation that would satisfy this table of values if we let m represent the number of miles and A represent the amount of money collected? # of milesAmount of $ Collected Excellent…A = 5 +.5m mA

Solving Problems Using Equations Given the equation below for Alana’s Pledge Plan, what would we do first to determine how many miles it would take to collect $8 from each sponsor? A = 5 +.5mNice…plug in 8 for A.8 What is the first algebraic step you should do to solve this problem? Great…subtract 5 from both sides. – 5.5m3= .5 6m= What is the second algebraic step to solve this equation? Beautiful…divide both sides by.5! 8 = 5 +.5(6) It works! Don’t forget to check your solution!

Partner Work You have 15 minutes to work on the following questions with your partner.

For those that finish early 1. Five more than twice a number is 27. Write an equation to solve for the unknown number. 2. Twelve year old Aaron O’Leary of Columbus, Ohio, bought old bikes at an auction for $350. He fixed them and sold them for $50 each. He made a $6200 profit. a) Write an equation for this situation that shows the relationship between profit and the number of bikes sold. b) Determine how many bikes he sold using the equation.

Big Ideas from Today’s Lesson You use the inverse operations of addition and subtraction, multiplication and division to solve equations that involve two steps. The order in which you undo the actions matters.

Homework Complete Homework Worksheet Pgs. 123 – 124 (13 – 37 odd, 47, 52, 53)