 # Solving Equations with Variables on Both Sides

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Solving Equations with Variables on Both Sides
Warm Up Lesson Presentation Lesson Quiz Holt Algebra 1 Holt McDougal Algebra 1

Warm Up Simplify. 1. 4x – 10x 2. –7(x – 3) 3. –6x 4. 15 – (x – 2)
Solve. 5. 3x + 2 = 8 6. –6x –7x + 21 2x + 3 17 – x 2 28

Homework Check: Kuta WS
1) a=16 13) m = 5 3) x = 0 15) n = 3 5) r = 20 17) n = 11 7) v =15 21) n = 0 9) x = 9 23) b = 12 11) v = -16

Notebook Organization
Notebook/Graph paper in front Dividers (in this order): Warm-Up/Closings Notes Classwork Homework Quiz/Test Review EOCT Review

Objective Solve equations in one variable that contain variable terms on both sides.

To solve an equation with variables on both sides, use inverse operations to "collect" variable terms on one side of the equation. Helpful Hint Equations are often easier to solve when the variable has a positive coefficient. Keep this in mind when deciding on which side to "collect" variable terms.

Example 1: Solving Equations with Variables on Both Sides
Solve 7n – 2 = 5n + 6. 7n – 2 = 5n + 6 To collect the variable terms on one side, subtract 5n from both sides. –5n –5n 2n – 2 = 2n = Since n is multiplied by 2, divide both sides by 2 to undo the multiplication. n = 4

Check It Out! Example 1a Solve 4b + 2 = 3b. 4b + 2 = 3b To collect the variable terms on one side, subtract 3b from both sides. –3b –3b b + 2 = 0 – 2 – 2 b = –2

Check It Out! Example 1b Solve y = 0.7y – 0.3. To collect the variable terms on one side, subtract 0.3y from both sides. y = 0.7y – 0.3 –0.3y –0.3y = 0.4y – 0.3 Since 0.3 is subtracted from 0.4y, add 0.3 to both sides to undo the subtraction. = 0.4y Since y is multiplied by 0.4, divide both sides by 0.4 to undo the multiplication. 2 = y

Whiteboard Problem Solve for x. 7x + 2 = 5x + 8 3

To solve more complicated equations, you may need to first simplify by using the Distributive Property or combining like terms.

Example 2: Simplifying Each Side Before Solving Equations
Solve 4 – 6a + 4a = –1 – 5(7 – 2a). 4 – 6a + 4a = –1 –5(7 – 2a) Distribute –5 to the expression in parentheses. 4 – 6a + 4a = –1 –5(7) –5(–2a) 4 – 6a + 4a = –1 – a 4 – 2a = – a Combine like terms. Since –36 is added to 10a, add 36 to both sides. 40 – 2a = a + 2a a To collect the variable terms on one side, add 2a to both sides. = a

Example 2 Continued Solve 4 – 6a + 4a = –1 – 5(7 – 2a). 40 = 12a Since a is multiplied by 12, divide both sides by 12.

Check It Out! Example 2b Solve 3x + 15 – 9 = 2(x + 2). 3x + 15 – 9 = 2(x + 2) Distribute 2 to the expression in parentheses. 3x + 15 – 9 = 2(x) + 2(2) 3x + 15 – 9 = 2x + 4 3x + 6 = 2x + 4 Combine like terms. –2x –2x To collect the variable terms on one side, subtract 2x from both sides. x + 6 = – – 6 Since 6 is added to x, subtract 6 from both sides to undo the addition. x = –2

Whiteboard Problem Solve for x. 4(2x – 5) = 5x + 4 8

Whiteboard Problem Solve for a. 6 – 7(a + 1) = –3(2 – a)

You will complete 4 problems at a time
You will complete 4 problems at a time. You must have your work checked before you may proceed. The problems you do not complete will be your homework for today. Closing: Our first quiz will be on Friday. What will you do to prepare for it? Classwork: STOP!