example 1 collecting like terms x + 2 = 3x x + 2 –x = 3x – x 2 = 2x 1 = x original equation...

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EXAMPLE 1 Collecting Like Terms x + 2 = 3x x + 2 –x = 3x – x 2 = 2x 1 = x Original equation Subtract x from each side. Divide both sides by 2. 2 2 2x 2 =

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Page 1: EXAMPLE 1 Collecting Like Terms x + 2 = 3x x + 2 –x = 3x – x 2 = 2x 1 = x Original equation Subtract x from each side. Divide both sides by 2. 2 2 2x2x

EXAMPLE 1 Collecting Like Terms

x + 2 = 3x

x + 2 –x = 3x – x

2 = 2x

1 = x

Original equation

Subtract x from each side.

Divide both sides by 2.

22

2x2=

Page 2: EXAMPLE 1 Collecting Like Terms x + 2 = 3x x + 2 –x = 3x – x 2 = 2x 1 = x Original equation Subtract x from each side. Divide both sides by 2. 2 2 2x2x

EXAMPLE 2 Solve a Multi-Step Problem

Each side of the triangle has the same length. What is the perimeter of the triangle?

SOLUTION

5x + 9 = 7x + 5 Write an equation.

5x + 9 –5x = 7x + 5 –5x Subtract 5x from each side.

9 = 2x + 5 Simplify.

9 –5 = 2x + 5–5 Subtract 5 from each side.

4 = 2x Simplify.42

2x2= Divide each side by 2

2 = x Simplify.

Page 3: EXAMPLE 1 Collecting Like Terms x + 2 = 3x x + 2 –x = 3x – x 2 = 2x 1 = x Original equation Subtract x from each side. Divide both sides by 2. 2 2 2x2x

EXAMPLE 2 Solve a Multi-Step Problem

Because 5x + 9 = 5(2) + 9 = 19, each side of the triangle is 19 units long. Since each side of the triangle has the same length, the perimeter is 3 19, or 57 units.

The perimeter of the triangle is 57 units.

ANSWER

Page 4: EXAMPLE 1 Collecting Like Terms x + 2 = 3x x + 2 –x = 3x – x 2 = 2x 1 = x Original equation Subtract x from each side. Divide both sides by 2. 2 2 2x2x

EXAMPLE 3 Using the Distributive Property

21x = 3(2x + 30) Original equation.

21x –6x = 6x + 90 –6x Subtract 6x from each side.

15x = 90 Simplify.

Divide each side by 15

x = 6 Simplify.

21x = 6x + 90 Distributive property

1515x15

90=

Page 5: EXAMPLE 1 Collecting Like Terms x + 2 = 3x x + 2 –x = 3x – x 2 = 2x 1 = x Original equation Subtract x from each side. Divide both sides by 2. 2 2 2x2x

GUIDED PRACTICE for Examples 1, 2, and 3

55 + 3x = 8x1.

11 = x

Solve the equation.

Page 6: EXAMPLE 1 Collecting Like Terms x + 2 = 3x x + 2 –x = 3x – x 2 = 2x 1 = x Original equation Subtract x from each side. Divide both sides by 2. 2 2 2x2x

GUIDED PRACTICE for Examples 1, 2, and 3

9x = 12x – 92.

x = 3

Page 7: EXAMPLE 1 Collecting Like Terms x + 2 = 3x x + 2 –x = 3x – x 2 = 2x 1 = x Original equation Subtract x from each side. Divide both sides by 2. 2 2 2x2x

GUIDED PRACTICE for Examples 1, 2, and 3

–15x + 120 = 15x3.

4 = x

Page 8: EXAMPLE 1 Collecting Like Terms x + 2 = 3x x + 2 –x = 3x – x 2 = 2x 1 = x Original equation Subtract x from each side. Divide both sides by 2. 2 2 2x2x

GUIDED PRACTICE for Examples 1, 2, and 3

4. 4a + 5 = a + 11

2 = a

Page 9: EXAMPLE 1 Collecting Like Terms x + 2 = 3x x + 2 –x = 3x – x 2 = 2x 1 = x Original equation Subtract x from each side. Divide both sides by 2. 2 2 2x2x

GUIDED PRACTICE for Examples 1, 2, and 3

n = –8

3n + 7 = 2n –15.

Page 10: EXAMPLE 1 Collecting Like Terms x + 2 = 3x x + 2 –x = 3x – x 2 = 2x 1 = x Original equation Subtract x from each side. Divide both sides by 2. 2 2 2x2x

GUIDED PRACTICE for Examples 1, 2, and 3

–6c + 1 = –9c + 76.

c = 2

Page 11: EXAMPLE 1 Collecting Like Terms x + 2 = 3x x + 2 –x = 3x – x 2 = 2x 1 = x Original equation Subtract x from each side. Divide both sides by 2. 2 2 2x2x

GUIDED PRACTICE for Examples 1, 2, and 3

5 = s

28 –3s = 5s –127.

Page 12: EXAMPLE 1 Collecting Like Terms x + 2 = 3x x + 2 –x = 3x – x 2 = 2x 1 = x Original equation Subtract x from each side. Divide both sides by 2. 2 2 2x2x

GUIDED PRACTICE for Examples 1, 2, and 3

w = –18

4(w – 9) = 7w + 188.

Page 13: EXAMPLE 1 Collecting Like Terms x + 2 = 3x x + 2 –x = 3x – x 2 = 2x 1 = x Original equation Subtract x from each side. Divide both sides by 2. 2 2 2x2x

GUIDED PRACTICE for Examples 1, 2, and 3

y = –3

9. 2(y + 4) = –3y – 7

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