Welcome To GED On Line Lessons Welcome To GED On Line Lessons By Christian Okolo DPS Adult Education East Campus, Detroit. Microsoft Clip Art

Lesson: Solving Linear Equations. What is Linear Equation? Linear equation is an equation that generates a straight line when plotted on a graph paper: X

Michigan Curriculum Standard: Michigan Curriculum Standard: Standard V.1: Operations and their Properties. Students understand and use various types of operations (e.g., addition, subtraction, multiplication, and division) to solve problems. Standard V.2: Algebraic and Analytic Thinking. Students analyze problems to determine the appropriate process for solution, and use algebraic notations to model or represent problems. X

ISTE Standard: ISTE Standard: Standard 4 Critical thinking, problem solving, and decision making. Students use critical thinking skills to plan and conduct research, manage projects, solve problems, and make informed decisions using appropriate digital tools and resources. X

Materials for the lesson: Materials for the lesson: Pen, pencils, paper, work sheet, white board, computer, over head projector. The over head projector will be used to show a video of the application of linear equations in real life. X

Classroom Set Up Classroom Set Up This lesson is design for a diverse classroom with students of various learning styles. Students can work in groups or as individuals. X

Objective: Objective: By the end of this lesson students will be able to solve One-step, Two- Step, and Multi- Step Linear Equations. X

Procedure: Procedure: Solving linear equation is like balancing the scale: Place all letters on the left arm of the scale and all numbers on the right arm of the scale as shown. The equal sign is the pivot of the scale. Add and subtract numbers and letters on both sides of the scale to balance the equation. X = 2, , 45 x, y, n,

Examples: Examples: Solve the following equations: Ex 1. 6x = 12 EX 2. 5x + 2 = 3x + 10 EX 3. 4(y – 2) = 2(y + 4) X

Example 1: 6x = 12 Example 1: 6x = 12 This is One-Step Equation. Step: Divide both sides of the equation by 6; then simplify by cancelling the denominators and numerators on both sides of the equation: 6x = 12 6 Answer: x = 2 X

Example 2: 5x + 2 = 3x + 10 This is Two-Step-Equation. Step 1: Move all letters to the left side of the equal sign and all numbers the right side of the equal sign as shown: 5x – 3x = 10 – 2 2x = 8 Step2: Divide both sides by 2: 2x/2 = 8/2 x = 4 X

Example 3: 4(y – 2) = 2(y + 4) This is Multi-Step-Equation. Step 1 Apply distributive property by multiplying numbers in the parenthesis as shown: 4(y – 2) = 2(y + 4) 4y – 8 = 2y + 8 Now, bring like terms together by balancing the equation: X

Step 2 Step 2 We balance the equation by Adding and subtracting on both sides of the equation as shown: 4y – 8 = 2y + 8 –2y +8 = –2y + 8 2y 0 = 0 16 We have: 2y = 16 X

Step 3 Step 3 Divide both sides of the equation by the coefficient of ''y'': The coefficient is always the number in front of the letter; we have: 2y = 16 2 Answer: y = 8 X

In Class Practice In Class Practice Now that you know how to solve linear equations, you must solve the following problems to see if you mastered the skills presented in this lessons. Get a scratch piece of paper and solve following equations. X

Solve the following equations Solve the following equations 1. 4(m + 3) = 3(m – 3) 2. 8(3x – 5) = 10 – 2x 3. 2(z + 3) = 5(2z-2)-12 Answer Key: 1. m= x= 25/13 3. z= 7/2 X

Special Accommodations Students with disabilities and slow learners will be given extra time to complete their work. For help with home work assignments, visit: X

Home work Assignment Home work Assignment Complete the following problems as soon as possible. 1. 6(x – 2) = 4 + 2x 2. 5(x – 1) = 2(7 + x) 3. 4(y + 5) = 3(y – 4) 4. 7x – 8 = (4m + 3) = m X

Answer Key: Home work Assignment 1. x =4 2. x = 19/3 3. y = x = 4 5. m = 1 Now that you know how to solve equations, you are ready for our Algebra Contest. X

Next is our Algebra: Contest Next is our Algebra: Contest To compete in the Algebra contest you must complete all the home work assignment with a min. score of 90%. This is the time for you to prove that you are a champion in Algebra. Earn your bragging right by completing the problems on time. Speed and accuracy is the key to success in Algebra tests. X

Contest Instructions Get a scratch piece paper click on any of the problems on the menu. Solve the problem immediately and check your answer. If you get an applause that means your answer is correct. If you get and evil laugh, or elephant walk; that means your answer is wrong. You must re-do the problem immediately. You can work as a group or as individuals. X

Contest Menu Contest Menu Problem points Problem points Problem points Problem points X Problem points Problem points

100 points: Solve the equation for x 12x = 60 x=? D C B A X

125 Point: Solve for x 125 Point: Solve for x Solve: 12x + 7 = 3x – 20; x = ? 9x 7 10 – 3 D C B A X

250 Point: Solve the equation for m 250 Point: Solve the equation for m Solve: 5(m + 4) = 7(m – 2) m =? m = 10 m = -15 m = 17 m = 2 D C B A X

275 Point: Solve for y 275 Point: Solve for y Solve: 4(3y - 2)=4(y+2)+2y-3 y =? y = 4 y = 1/2 y = 3 y = 13/6 D C B A X

350 Point: Solve for z 350 Point: Solve for z Solve: 2(4z - 3)=4(z+1)+3(2z-2) z =? z = 4 z = 8 z = -2 z = 3 D C B A X

400 Point: Solve for m 400 Point: Solve for m Solve: 2(3m-2)=4(m+2)+ 2m-5 m =? m = 6 m =-5/2 m = 4/5 m = 5/4 D C B A X

That is Correct! That is Correct! Click on the Home Button to Return to Contest Menu X

Sorry! That is not the correct answer Sorry! That is not the correct answer Click the Return Button to go back to the previous slide. X

Sorry! That is not the correct answer Sorry! That is not the correct answer Click the Return Button to go back to the previous slide. X

THE END THE END This is the end of the contest. if you scored points, visit the Algebra Hall of Fame to claim your trophy. X Algebra Hall of Fame click here

ALGEBRA HALL OF FAME ALGEBRA HALL OF FAME X