ObjectivesVocabularyExample 1Example 2Example 3Quick Quiz

• To solve equations by adding, multiplying, or dividing both sides by the same quantity

• To describe variable quantities that appear in typical word problems, including those that refer to signed numbers

• To add and subtract parenthetical expressions

• conjecture

Solve 5x + 12 = 2x. Check your solution.

5x + 12 = 2xWrite the

equation.5x – 5x + 12 = 2x – 5x

Subtract 5x from each side.

12 = –3xSimplify.

–4 = x Mentally divide each side by –3.

Subtract 5x from the left side of the equation to isolate the variable.

Subtract 5x from the right side of the equation to keep it balanced

To check your solution, replace x with –4 in the original equation.

Check 5x + 12 = 2x

Write the equation.

Answer: The solution is –4.

5(–4) + 12 = 2(–4)Replace x with –4.

?

–20 + 12 = –8

Simplify.

?

–8 = –8

This statement is true.

Solving Equations

1. A2. B3. C4. D0% 0%0%0%

Solve 7x = 5x + 6. Check your solution.

A. –3

B.

C. 3

D. 21

A. Solve 3h = 5(h – 2). Check your solution.

3h = 5(h – 2) Write the

equation. 3h = 5(h) – 5(2)

Use the Distributive Property.

3h = 5h – 10Simplify.

3h – 5h = 5h – 5h – 10Subtract 5h

from each side. –2h = –10

Simplify.

Divide each side by –2.

h = 5 Simplify.

Check 3h = 5(h – 2)

Write the equation.

Answer: The solution is 5.

3(5) = 5(5 – 2)Replace h

with 5.

?

? 15 = 5(3)

Simplify. 15 = 15

This statement is true.

Two-Step Equations

B. Solve 6(b – 2) = 3(b + 8.5). Check your solution.

6(b – 2) = 3(b + 8.5) Write the

equation. 6b – 12 = 3b + 25.5

Use the Distributive Property.

6b – 3b – 12 = 3b – 3b + 25.5 Subtract 3b from each side.

3b – 12 = 25.5Simplify.

3b – 12 + 12 = 25.5 + 12Add 12 to

each side. 3b = 37.5

Simplify.

Divide each side by 3.

b = 12.5Simplify.

Answer: The solution is 12.5.

1. A2. B3. C4. D

A B C D

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A. Solve 4t = 7(t – 3). Check your solution.

A. –7

B. 1

C.

D. 7

1. A2. B3. C4. D

A B C D

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B. Solve 3(p + 5) = 6(p – 2). Check your solution.

A. 9

B. 8

C.

D.

GEOMETRY The perimeter of a rectangle is 36 inches. Find the dimensions if the length is 2 inches greater than three times the width.Words 2 times the length + 2 times the width =

perimeter

Variable Let w = the width.Let 3w + 2 = the length.

Equation 2(3w + 2) + 2w = 36

3w + 2

w

2(3w + 2) + 2w = 36 Write the equation. 6w + 4 + 2w = 36

Use the Distributive Property.

8w + 4 = 36Simplify.

8w + 4 – 4 = 36 – 4Subtract

4 from each side. 8w = 32

Simplify. w = 4

Mentally divide each side by 8.

Evaluate 3w + 2 to find the length.3(4) + 2 = 12 + 2 or 14 Replace w with 4.

Answer: The width is 4 inches. The length is 14 inches.

1. A2. B3. C4. D

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GEOMETRY The perimeter of a rectangle is 26 feet. Find the dimensions if the length is 2 feet less than twice the width.

A.

B.

C. width = 5 ft; length = 8 ft

D. width = 11 ft; length = 24 ft

1. A2. B3. C4. D

A. An airplane climbs at a rate of n feet per minute. The same airplane glides down to Earth without power at a rate of q feet per minute. Select an expression describing the change in altitude if it first climbs for 5 minutes and then glides for 2 minutes.A. 5n + 2q

B. 5n – 2q

C. 5n – q

D. n + 5 – 2q

1. A2. B3. C4. D

A B C D

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B. The same airplane starts at 5,000 feet above sea level. It climbs for 10 minutes and then glides to earth for 8 minutes. Select an expression that describes the glider’s altitude above sea level at that point.

A. 5,000 + n – q

B. 5,000 – 10n + 8q

C. 5,000 + 10n – 8q

D. 5,000 + 10 – 8

1. A2. B3. C4. D

A B C D

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A. Select the correct expression without parentheses for 2 – 3(4 – 6). Then evaluate the expression.

A. 2 – 12 + 18; 8

B. 2 – 12 – 24; –34

C. 8 – 12 – 18; –22

D. 2 + 18 – 24; –4

1. A2. B3. C4. D

A B C D

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B. Select the correct expression without parentheses for – 7 + (–2 + 3). Then evaluate the expression.

A. –7 – 2 + 3; –6

B. –7 + 14 – 21; –14

C. –7 – 14 + 21; 0

D. –7 + 2 – 3; –8

1. A2. B3. C4. D0% 0%0%0%

Simplify 5n – 3(2 – 6n).

A. 23n – 6

B. 23n + 6

C. 13n – 6

D. 13n + 6

1. A2. B3. C4. D

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Solve the equation 3g + 2(6 – g) = 4 + 5(g + 1).

A.

B. g = 3

C.

D. g = 4

Image Bank

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Solving Equations Using Algebra Tiles

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Solving Equations Two-Step Equations