Holt McDougal Algebra 1

Solving Equations with Variables on Both Sides

Solving Equations with Variables on Both Sides

Holt Algebra 1

Warm UpWarm Up

Lesson PresentationLesson Presentation

Lesson QuizLesson Quiz

Holt McDougal Algebra 1

Holt McDougal Algebra 1

Solving Equations with Variables on Both Sides

Warm UpSimplify.

1. 4x – 10x

2. –7(x – 3)

3.

4. 15 – (x – 2)

Solve.

5. 3x + 2 = 8

6.

–6x–7x + 21

17 – x

2x + 3

2

28

Holt McDougal Algebra 1

Solving Equations with Variables on Both Sides

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

Holt McDougal Algebra 1

Solving Equations with Variables on Both Sides

Notebook Organization

• Notebook/Graph paper in front

• Dividers (in this order): – Warm-Up/Closings– Notes– Classwork– Homework– Quiz/Test Review– EOCT Review

Holt McDougal Algebra 1

Solving Equations with Variables on Both Sides

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

Objective

Holt McDougal Algebra 1

Solving Equations with Variables 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 HintEquations 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.

Holt McDougal Algebra 1

Solving Equations with Variables on Both Sides

Solve 7n – 2 = 5n + 6.

Example 1: Solving Equations with Variables on Both Sides

To collect the variable terms on one side, subtract 5n from both sides.

7n – 2 = 5n + 6

–5n –5n

2n – 2 = 6

Since n is multiplied by 2, divide both sides by 2 to undo the multiplication.

2n = 8

+ 2 + 2

n = 4

Holt McDougal Algebra 1

Solving Equations with Variables on Both Sides

Solve 4b + 2 = 3b.

Check It Out! Example 1a

To collect the variable terms on one side, subtract 3b from both sides.

4b + 2 = 3b

–3b –3b

b + 2 = 0

b = –2

– 2 – 2

Holt McDougal Algebra 1

Solving Equations with Variables on Both Sides

Whiteboard Problem

Solve for x.

7x + 2 = 5x + 8

3

Holt McDougal Algebra 1

Solving Equations with Variables on Both Sides

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

Holt McDougal Algebra 1

Solving Equations with Variables on Both Sides

Solve 4 – 6a + 4a = –1 – 5(7 – 2a).

Example 2: Simplifying Each Side BeforeSolving Equations

Combine like terms.

Distribute –5 to the expression in parentheses.

4 – 6a + 4a = –1 –5(7 – 2a)

4 – 6a + 4a = –1 –5(7) –5(–2a)

4 – 6a + 4a = –1 – 35 + 10a

4 – 2a = –36 + 10a

+36 +36

40 – 2a = 10a+ 2a +2a

40 = 12a

Since –36 is added to 10a, add 36 to both sides.

To collect the variable terms on one side, add 2a to both sides.

Holt McDougal Algebra 1

Solving Equations with Variables on Both Sides

Solve 4 – 6a + 4a = –1 – 5(7 – 2a).

Example 2 Continued

40 = 12a

Since a is multiplied by 12, divide both sides by 12.

Holt McDougal Algebra 1

Solving Equations with Variables on Both Sides

Solve 3x + 15 – 9 = 2(x + 2).

Check It Out! Example 2b

Combine like terms.

Distribute 2 to the expression in parentheses.

3x + 15 – 9 = 2(x + 2)

3x + 15 – 9 = 2(x) + 2(2)

3x + 15 – 9 = 2x + 4

3x + 6 = 2x + 4

–2x –2x

x + 6 = 4 – 6 – 6

x = –2

To collect the variable terms on one side, subtract 2x from both sides.

Since 6 is added to x, subtract 6 from both sides to undo the addition.

Holt McDougal Algebra 1

Solving Equations with Variables on Both Sides

Whiteboard Problem

Solve for x.

4(2x – 5) = 5x + 4

8

Holt McDougal Algebra 1

Solving Equations with Variables on Both Sides

Whiteboard Problem

Solve for a.

6 – 7(a + 1) = –3(2 – a)

Holt McDougal Algebra 1

Solving Equations with Variables on Both Sides

Classwork: STOP!• 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?