*KEY* Solving Linear Equations Worksheet *Point values for each question are in parentheses. 1.(4) List the steps for solving linear equations. 1) Simplify the equation. 2) Get the variable term on one side by itself. 3) Isolate the variable. 4) Check your answer. Solve the following linear equations. Show all steps and be sure to check your work. 2.(2) 2x + 4 = 10 -4 -4 Check: 2x = 6 2(3) + 4 = 10 2x/2 = 6/2 6 + 4 = 10 x=3 10 = 10 D 3.(2) 4(x - 2) + 3x = 20 4x - 8 + 3x = 20 Check: 7x - 8 = 20 4(4 - 2) + 3(4) = 20 +8 +8 4(2) + 3(4) = 20 7x = 28 8 + 12 = 20 x=4 20 = 20 D 4.(2) 5(x - 1) + 1 = 3 + 2x 5x - 5 + 1 = 3 + 2x Check: 5x - 4 = 3 + 2x 5(7/3 - 1) + 1 = 3 + 2(7/3) +4 +4 5(4/3) + 1 = 3 +2(7/3) 5x = 7 + 2x 20/3 + 1 = 3 + 14/3 -2x -2x 23/3 = 23/3 D 3x = 7 3x/3 = 7/3 x = 7/3 5.(2) 12(3x + 1) = 24 36x + 12 = 24 Check: -12 -12 12[3(1/3) + 1] = 24 36x = 12 12(1 + 1) = 24 36x/36 = 12/36 12(2) = 24 x = 12/36 24 = 24 D x = 1/3 6.(3) 2(3x - 7) + 4 (3 x + 2) = 6 (5 x + 5) Check: 6x - 14 + 12x + 8 = 30x + 30 2[3(-3) - 7] + 4[3(-3) + 2] = 6[5(-3) + 5] 18x - 6 = 30x + 30 2(-9 - 7) + 4(-9 + 2) = 6(-15 + 5) +6 +6 2(-16) + 4(-7) = 6(-10) 18x = 30x + 36 -32 + -28 = -60 -30x -30x -60 = -60 D -12x = 36 -12x/-12 = 36/-12 x = -36/12 x = -3 Solve the following story problems by using linear equations. 7.(2) Together, Sally and Sam bought a total of 15 apples. If Sally bought 6 apples, how many did Sam buy? Use x as your variable to set up the equation, then solve. 6 + x = 15 Check: -6 -6 6 + 9 = 15 Sam bought 9 apples. x=9 15 = 15 D 8.(3) Billy is 12 years old. He is 4 times as old as his little brother. How old is Billy’s little brother? Use x as your variable to set up the equation, then solve. 4x = 12 Check: 4x/4 = 12/4 4(3) = 12 Billy’s brother is 3 years old. x=3 12 = 12 D Solving Linear Equations Lesson: Solving Linear Equations Length: 45 minutes Age or Grade Level Intended: High School - 9th grade Academic Standard(s): A1.2.1 Solve linear equations Performance Objective(s): Given linear equations, students will solve the equations using the appropriate methods with 90 percent accuracy. Assessment: Students will be given a worksheet on solving linear equations for homework. They will complete the homework and turn it in at the beginning of class the next day. Advanced Preparation by Teacher: The teacher will need to create a worksheet worth 20 points on solving linear equations to be given out for homework. The teacher will also need to prepare at least twenty incomplete math sentences for the board races and make sure there is enough chalk at the board. Procedure: IntroductionBoard Races - Students will be paired up and asked to find a space at the chalk board. The teacher will then ask them to write down a predetermined incomplete math sentence. When the teacher says “go”, the students will work together as partners against the other pairs. Once a pair has completed the sentence, they will raise their hands. First pair to raise their hands and have the correct answer will receive one point. First pair to 5 points wins. Example incomplete math sentences: __ + 5 = 34 __ - 7 = 18 15 - __ = -2 3/2 + __ = 5/4 *Be sure to increase the difficulty as you go. (Gardner: Visual-Spatial, Logical-Mathematical, and Interpersonal Intelligences) Plan1. Ask the students what a equation is. (Bloom: Level I - Knowledge) 2. Define equation: An equation is two expressions set equal to each other. To demonstrate this, use a couple of the completed math sentences from the Board Race activity. 3. Now define a linear equation: Is an equation that is in the form ax + b = c where a, b, and c are any value. The value of the unknown variable x is what we are looking for when solving linear equations. 4. How do you solve linear equations? (Bloom: Level III-Application) A) Simplify the equation by using the distribution property and combining like terms. B) Use addition and subtraction properties to get the variable term to one side by itself. Remember that what you do to one side, you must do the same to the other. C) Now use multiplication and division properties to isolate the variable (get x by itself). D) Plug the value you received for the variable (x) back into the original equation to check your answer. 5. Now give some examples of solving linear equations using these steps. Example 1 3x + 1 = 4 A) Simplify the equation. This equation is already simplified. 3x + 1 = 4 B) Get the variable term on one side by itself. 3x + 1 = 4 -1 -1 Subtract 1 from both sides. 3x = 3 C) Isolate the variable. 3x = 3 3x/3 = 3/3 Divide each side by 3. x=1 D) Check your answer. Plug the value of x back into the original equation. 3(1) + 1 = 4 3+1=4 4=4 Example 2 2(x - 1) + x = 10 A) Simplify the equation. 2(x - 1) + x = 10 2x - 2 + x = 10 Distribute the 3. 3x - 2 = 10 Combine like terms. B) Get the variable term on one side by itself. 3x - 2 = 10 +2 +2 Add 2 to both sides. 3x = 12 C) Isolate the variable. 3x = 12 3x/3 = 12/3 Divide each side by 3. x=4 D) Check your answer. 2(4 - 1) + 4 = 10 2(3) + 4 = 10 6 + 4 = 10 10 = 10 Example 3 10(x -2) + 2 = 6 + 2x A) Simplify the equation. 10(x -2) + 2 = 6 + 2x 10x - 20 + 2 = 6 + 2x Distribute the 10. 10x - 18 = 6 + 2x Combine like terms. B) Get the variable term on one side by itself. 10x - 18 = 6 + 2x -2x -2x Subtract 2x from both sides. 8x - 18 = 6 +18 +18 Add 18 to both sides. 8x = 24 C) Isolate the variable. 8x = 24 8x/8 = 24/8 Divide each side by 8. x=3 D) Check your answer. 10(3 - 2) + 2 = 6 + 2(3) 10(1) + 2 = 6 + 2(3) 10 + 2 = 6 + 6 12 = 12 ClosureHave the students pair back up, this time at their desks. Ask them to create and solve their own linear equation. Be sure to walk around and answer any questions they might have. Once they are done, pass out the worksheet on linear equations for homework. Have them complete it and turn in at the beginning of class the next day. (Bloom: Level V-Synthesis) (Gardner: LogicalMathematical and Interpersonal Intelligences) Adaptations/Enrichments: Learning disabilities in reading comprehension - No reading from the book is required for this lessons. Instructions on how to solve linear equations are written on the board, however oral instructions are also given. ADHD - The board races at the beginning of the lesson allows this student to move around. During the lesson, this student, if needed, can come up to the board to help solve the example problems. Gifts/Talents in Creativity - Encourage this student to lead their pair when it is time to create their own equation. Have the student think of a way to remember the steps in solving linear equations. Self-Reflection: Were the board races an effective attention getter? How time consuming were the board races? How many students understood this lesson? Are the students able to solve linear equations? Were the students able to create their own equations? Did the students cooperate with each other? How does this tie into the next lesson? Did I engage the whole class? What would I do differently next time to improve the lesson. Solving Linear Equations Worksheet *Point values for each question are in parentheses. 1.(4) List the steps for solving linear equations. Solve the following linear equations. Show all steps and be sure to check your work. 2.(2) 2x + 4 = 10 3.(2) 4(x - 2) + 3x = 20 4.(2) 5(x - 1) + 1 = 3 + 2x 5.(2) 12(3x + 1) = 24 6.(3) 2(3x - 7) + 4 (3 x + 2) = 6 (5 x + 9) + 3 Solve the following story problems by using linear equations. 7.(2) Together, Sally and Sam bought a total of 15 apples. If Sally bought 6 apples, how many did Sam buy? Use x as your variable to set up the equation, then solve. 8.(3) Billy is 12 years old. He is 4 times as old as his little brother. How old is Billy’s little brother? Use x as your variable to set up the equation, then solve.