Solving Linear Equations

Transcription

1 Success Center Directed Learning Activity (DLA) Solving Linear Equations M108.1

2 Directed Learning Activity Solving Linear Equations Description: In this Directed Learning Activity (DLA), you will learn how to solve a linear equation. The DLA will: 1) describe linear equations, 2) show how to solve basic equations, and 3) show how to convert more complicated equations into basic equations. Prior Knowledge: In order to complete this DLA, you will need to understand how to solve a simple equation. Simple Equations: Isolating the x. In order to isolate the x, we must remove the number on the x-side We subtract a 3 from both sides to remove the 3 from the x-side. Thus, x is isolated on one side of the equation; the final answer for the first example is x = 14. Solve these simple equations as a warm up. X 7 2 x 5 4 8X 24 2 X 7 Materials: A scientific calculator may be needed. Directions: Please read the examples and answer the questions that follow carefully and in order. Please do not skip ahead. If you have a question, please ask for help. After reading the examples in the boxes below, spend some time thinking about what is being presented. After you feel you understand the examples, try to answer the practice questions. When you are finished, review the DLA with a tutor or an instructor. Don t worry: You are not being graded. This is a learning activity, and you are not expected to know everything. Part One: Understanding What an Equation Is An equation is a question that asks you to find a missing value. Let s look at our first example. What number plus 4 equals 7? After reading the question, we might guess that x = 3. Rules of the game: 1) There are two sides to an equation: one side on the left of the equal sign and one on the right. 2) What you do to one side of the equation, you must do to the other. 3) You want to try to isolate the x to make the x the only object on its side.

3 Part Two: Solving Basic Equations The 3, 2,and 8 are all quantities. The 3x is 3 times x, so it could be read as 3 xs or x + x + x. The 2 and 8 are constants and could be thought of as a quantity of apples. x + x + x = x + x + x = x = x=2 We subtract or remove two apples from both sides to keep the equation. equal. We then divide both sides by 3 dividing each side into three parts. We can now see by comparison that one x is equal to two apples, so x = 2. The pattern is similar in most linear equations. We add or subtract to isolate our x. Then we divide by the number of xs we have. 1) Isolate the x. (xs on one side, non-xs on the other) (add and subtract) 2) Divide. (divide by the number next to the variable) Try to apply what you have learned so far by solving these two basic equations. a) b)

4 Part Three: Simplifying Basic Equations S-I-D 1) Simplify 2 3x 8 18( 1) (simplify each side) i) Distribute/Multiply ii) Combine Like Terms x 2 2x ) Isolate the x 3) Divide Try to apply what you have learned so far by simplifying these two basic equations with the S-I-D (Simplify-Isolate-Divide) process shown above. a) b) Part Four: Converting Complicated Equations Into Basic Equations x-side 1) Simplify 3 8 2x 12 (simplify each side) i) Distribute/Multiply ii) Combine Like Terms We now have a basic equation. 2) Isolate the x (pick an x side) Remove 2x because it is not on the x-side. x 5( x 6) 7x x-side We now have a basic equation. 3) Divide 3 = x Try to apply what you have learned so far by converting these complicated equations into basic equations with the S-I-D process. a) b)

5 Part Five: Testing Your Knowledge a) b) c) d) e) f) Part Six: Reflection a) Name one thing that you understand better about solving linear equations as a result of completing this activity. b) Name one thing that you still do not understand about solving linear equations. c) What does 5x +7 = 2x - 3 really mean? STOP. Please go over your work with a tutor at this time.

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7 M108.1 Solving Linear Equations PRINT STUDENT NAME STUDENT # Tutor Feedback: The student completed the entire activity. The student attempted to answer every question. The student demonstrated an understanding of the processes necessary for solving linear equations during the discussion of his/her work. Additional Comments: PRINT INSTRUCTOR/TUTOR NAME DATE INSTRUCTOR/TUTOR SIGNATURE STUDENT DO NOT FORGET TO TURN THIS SHEET IN AT THE FRONT DESK! You may not get credit for completing this DLA if you fail to leave this sheet with the front desk receptionist.