CP –Algebra 1 Unit 1- Day 1 Notes date______________ Targets - Solve Multi-Step Equations 1. I can identify the like terms, coefficients and constant terms. 2. I can solve a multi-step equation (by combining like terms, with variables on both sides, and using inverse operations) and justify each step. 3. I can translate a word problem into an equation and solve. GOAL: To solve equations that have both variables and whole numbers on each side of the equation (equal sign). Inverse operations will be used to move the necessary variable and whole number to the needed side of the equal sign so that the variable will be on one side, and the whole numbers (without variables) will be on the other side. For example, x = 4. Warm-Up: Solve the following one-step equations. a. 6 = 9 + h b. x - 7 = 4 d. 6 = c. e. − 3 = 9 7 6w = -54 f. 5 6 = 10 Steps to solve a two-step equation 1) Use the inverse operation to isolate the variable (i.e. move the terms with variables to one side of the equation) 2) Use the inverse operation to solve for the variable. Solve an equation by using inverse operations to isolate the variable Solve 5x – 5 = 10 Steps 5x – 5 = 10 +5 + 5 5x = 15 5 5 Justification Use inverse operation of adding 5 to both sides to get the variable Use inverse operation of dividing by 5 on both sides to get x by itself x =3 Ex. 1 Solve each equation a. d. 2 + 5 = 11 b. 5x + 9 = 24 2 e. 2 − 9 = 11 10 = 7 + 4 c. 16 = 4y – 4 f. 10 = 7 − CP –Algebra 1 Unit 1- Day 2 Notes date______________ Targets - Solve Multi-Step Equations 1. I can identify the like terms, coefficients and constant terms. 2. I can solve a multi-step equation (by combining like terms, with variables on both sides, and using inverse operations) and justify each step. 3. I can translate a word problem into an equation and solve. Solve a two-step equation by first combining like terms and second using inverse operations Solve 7 − 4 = 21 Steps 7x – 4x = 21 3x = 21 3 3 x=7 Ex. 2 a. 6 − 2 = 28 Warm-Up: Justification Combine like terms (7x – 4x) Use inverse operation of dividing by 3 on both sides to get x by itself b. 6 + 3 = 36 5 1 c. 8 = 8 − 8 Simplify each expression by combining like terms a. 2x 7x b. 4a 8a c. 6x 8x 3x d. 4x 5 6x 2 e. 3x 10 3 11x f. 8 5x 2x 12 Steps to solve a multi-step equation 1) Simplify one or both sides of the equation 2) Then use inverse operations to isolate variable and justify. Solve an equation by combining like terms and justify Solve Steps Justification 3x + 5x – 5 = 11 8x – 5 = 11 5 +5 8x = 16 8 8 x =2 Ex 1 combine like terms on each side of the equal sign use inverse operation of adding 5 to both sides to get the variable alone on one side of the equal sign use inverse operation of dividing by 8 to get x by itself Solve each equation and justify each circled problem. a. 2x 7x 3 12 ______________________________________________________ ______________________________________________________ ______________________________________________________ b. 5x x 7 17 c. 10 2x 8 5x Solve an equation with variable on both sides and justify Solve 2x 3 x 2x 7 Steps Justification 2x + 3 + x = 2x + 7 3x + 3 = 2x + 7 - combine like term -2x -2x - inverse operation of subtracting 2x from both sides to move x+3=7 the variable to one side of the equal sign -3 -3 - inverse operation of subtracting 3 from both sides to move the whole number (number without a variable) to the OTHER x =4 side of the equal sign ‘ Ex 2 Solve each equation and justify each circled equation. a. 7x 4 3x 12 b. 7 x 5 2x 23 c. x 5 4x 2x 10 d. 2 x 14 3 e. 1 x 5 3 2 f. 1 2x x 8 2 g. 3 x 2 x 3 4 h. 5 x 2 3x 2 Ex 3 The perimeter of a triangle is 22 feet. The side lengths are x, 3x and 6 ft. Write an equation and solve for x. Ex 4 The length of a rectangle is 4 units more than 2 times the width. The perimeter is 32 units. Find the length and width of the rectangle described.

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