Solving Two-Step Equations Core Focus on Introductory Algebra Lesson 3.8

Solve each equation. Show all work and check your solution = x a = 603.k − 0.84 = The base of a triangle is 4 feet. The area of the triangle is 9 square feet. What is the height of the triangle? 5.The area of a rectangle is 400 square feet. Its width is 8 feet. What is the length of the rectangle? Warm-Up x = 24a = 4k = feet 50 feet

Solving Two-Step Equations Solve two-step equations. Lesson 3.8

Two-step Equation An equation with two different operations. Good to Know! In order to get the variable by itself you must perform TWO inverse operations. When solving a two-step equation, first you must balance the equation by undoing any ADDITION or SUBTRACTION. You can finish solving the equation by undoing any MULTIPLICATION or DIVISION. It is done in this order because it is undoing the order of operations. Vocabulary

Step 1If you do not have an equation mat, draw one like the one seen at right on a blank sheet of paper. Step 2On your equation mat place two variable cubes on one side with 4 chips. On the other side of the mat place 6 chips. What two-step equation does this represent? Step 3The first step to solving an equation is to remove the chips on the side with the variable. Remove an equal number of chips from BOTH sides of the mat. Draw a picture of what your mat looks like now. Step 4Divide the chips that are left on the mat equally between the two variable cubes. How many chips are equal to one cube? This is the value of x. Step 5Solve the equation 3x + 2 = 11 using the equation mat. What does x equal?

Solve each equation. Check the solution. a.7x − 3 = 74b. 7x − 3 = x = 77 7 a x = 11 Example 1 x = 18 – 5   7(11) − 3 = − 3 = = 74

Write an equation for the statement. Solve the problem and check the solution. a.Three times a number x increased by 8 is 29. Find the number x. Three times a number x  3x increased by 8  3x + 8 is 29  3x + 8 = 29 Example 2 3x + 8 = 29 – 8 – 8 3x = 21 3 a x = 7 a  3(7) + 8 = = = 29

Write an equation for the statement. Solve the problem and check the solution. b.Twice a number x minus 7 is 5. Find the number x. Twice a number x  2x minus 7  2x − 7 is 5  2x − 7 = 5 Example 2 Continued… 2x − 7 = x = 12 2 a x = 6 a  2(6) − 7 = 5 12 − 7 = 5 5 = 5

John and Erin shared a bag of chocolate candies. John ate five fewer than three times as many candies as Erin ate. If John ate 43 candies, how many candies did Erin eat? Let c represent the number of candies eaten by Erin. Write an equation to represent the situation. Solve the equation using inverse operations. Erin ate 16 candies. Example 3 3c − 5 = c = 48 3 a c = 16

What do you think are the most common mistakes students make when solving equations? Why do you think that? Communication Prompt

Solve for x. Check your solution. 1.3x + 1 = = 5x − 15 Exit Problems x = 6 x = 12 x = 7