Unit 6 Study Guide: Equations. Section 6-1: One-Step Equations with Adding & Subtracting

Transcription

1 Unit 6 Study Guide: Equations DUE DATE: A Day: Dec 18 th B Day: Dec 19 th Name Period Score / Section 6-1: One-Step Equations with Adding & Subtracting Textbook Reference: Page 437 Vocabulary: Equation a sentence stating that two quantities are equal Solution the value of a variable that makes the sentence true One-Step Equation an equation that can be solved in one step The goal of solving equations is to get the variable on one side and the constants on the other. To do this, you need to keep the balance between the two equal expressions. In other words, whatever you do to one side, you have to do to the other. Example 1 Solve 5 + x = 12 To solve this problem, we need to try to get x alone. This means that we need to subtract 5 from the left side; however, if we subtract 5 from the left side, we must subtract 5 from the right side to keep the balance between the two expressions. So: 5 + x = After we obtain a solution for x, we can then plug that answer back into the original equation to make sure that our answer is correct. So: = 12 x = 7 12 = 12 Since both sides equal the same thing, we know that x does equal 7. Example 2 Solve t 2 = 3 To solve this problem, we need to try to get alone. This means that we need to 2 to the left side; however, if we 2 to the left side, we must 2 to the right side to keep the balance between the two expressions. So: Solve on your own: t 2 = 3 Check your answer: 2 = 3 5=5 Page 1 of 5

2 Example 3 Solve r + ( 2) = 14 Example 4 Solve 5 w = 10 Section 6-2: One-Step Equations with Multiplying & Dividing Textbook Reference: Page 447 The Division property of Equality states that the two sides of an equation remain equal when you each side by the same nonzero number. The Multiplication property of Equality states that the two sides of an equation remain equal if you multiply each side by the same number. This means you can solve an equation for the unknown variable by multiplying or dividing each side of the equation by the same number (as long as it is not 0 ). Example 1 Example 2 Page 2 of 5

3 Example 3 Check the solution found in example 3: Now it s your turn. Solve for the variable in each equation. Write your answers as an integer or as a fraction in simplest form. 1. y 5 = = 6x x = 8 Section 6-3: Two-Step Equations Textbook Reference: Page 469 Recall that in solving equations: The must end up by itself on one side of the equal sign and the must all be moved to the other side of the equal sign. What you do to one side of the equal sign you. Steps to solving a 2-step equation 1. First, undo the by doing the opposite/inverse operation. 2. Then undo the multiplication or division by doing the opposite/inverse operation Check your answer by plugging it back into the original problem. Page 3 of 5

4 Examples: 1. 4x 3 = x = x = m + 4 = 2 3. y +1= i y 5 = 25 i 5 4. c 8 7 = 5 y = 125 Section 6-4: Multi-step Equations with Distributive Property Textbook Reference: Not in textbook Steps to solve a multi-step equation: 1. Simplify each side of the equation (if necessary) a. This includes using the distributive property and combining any like terms 2. If you have variables on both sides of the equal sign, get them on the same side. 3. Get the variable alone by adding or subtracting on both sides of the equation. 4. Multiply or divide on both sides to solve for the variable. 5. Check your answer by plugging the solution you found back into the original equation. Example 1: 2(x + 4) =10 2x + 8 = 10 (Use Distributive Property) x + 0 = 2 (Subtract 8 from both sides) 2x = 2 (Divide by 2) 2 2 X = 1 Check your solution by evaluating for x = 1 2((1) +4) = 10 2(5) = = 10 (Solution is good) Page 4 of 5

5 Example 2: 5x + 4-3x = 16 2x + 4 = 16 (Combine like terms) x + 0 = 12 (Subtract 4 from both sides) 2x = 12 (Divide by 2) 2 2 X=6 Check your solution by evaluating for x = 6 5(6) + 4-3(6) = = = = 16 Example 3: -3-3x + 2x = -8-3 x = -8 (Combine like terms) x + 0 = -5 (add 4 to both sides) -1x = -5 (Divide by -1) -1-1 X=5 Check your solution by evaluating for x = (5) + 2(5) = = = -8-8 = -8 Example 4: 2x + 7 = -3x x +3x 5x + 7 = x = X = -1 Check Solution: 2(-1) + 7 = -3(-1) = = 5 Solve on your own and be sure to check your answer. x = 2. 2x+ 3x+ 5= x+ 5= 3x ( 4) 4 Page 5 of 5