Algebra 2 Lesson 1-3 (Page 18) ALGEBRA 2 LESSON 1-3 Solving Equations 1-1.

Algebra 2Lesson 1-3(Page 18)

ALGEBRA 2 LESSON 1-3ALGEBRA 2 LESSON 1-3

Solving EquationsSolving Equations

1-1

To solve equations.



1-1

New Vocabulary



1-1

A number that makes the equation true is a

solution of the equation.

Properties of Equality (Page 18)



1-1

Solving EquationsSolving EquationsALGEBRA 2 LESSON 1-3ALGEBRA 2 LESSON 1-3

Solve 7x + 3 = 2x – 12.

7x + 3 = 2x – 12

5x + 3 = –12 Subtract 2x from each side.

5x = –15 Subtract 3 from each side.

x = –3 Divide each side by 5.

1-3

Check: 7x + 3 = 2x – 12

7(–3) + 3 2(–3) – 12

–18 = –18


Try this one on your own. Check your answer.

1-3

215128 zz



1-3

tt 4932


Solve 4(m + 9) = –3(m – 4).

4(m + 9) = –3(m – 4)

4m + 36 = –3m + 12 Distributive Property

7m + 36 = 12 Add 3m to each side.

7m = –24 Subtract 36 from each side.

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m = – Divide each side by 7.247



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706)3(2 y



1-3

)29(26)2(6 tt


The formula for the surface area of a rectangular prism

units long, w units wide, and h units high is A = 2( w + h + wh).

Solve the formula for w.

A = 2( w + h + wh)

A = 2 w + 2 h + 2wh Distributive Property

A – 2 h = 2 w + 2wh Subtract 2 h from each side.

A – 2 h = (2 + 2h)w Distributive Property

1-3

= w Divide both sides by 2 + 2h.A – 2 h2 + 2h



1-3

1

21

for equation theSolve2

1 : is trapezoida of areafor formula The

b

bbhA


Solve + 8 = b for x. Find any restrictions on a and b.xa

x + 8a = ab Simplify.

1-3

+ 8

= b

xa

a( ) + a(8) = ab Multiply each side by the least common denominator (LCD), a.

xa

x = ab – 8a Subtract 8a from each side.

=/The denominator cannot be zero, so a 0.



1-3

.for 015equation theSolve xbxax



1-3

.for 2

equation theSolve xba

xd

To solve problems by writing equations.



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Adrian will use part of a garage wall as one of the long sides

of a rectangular rabbit pen. He wants the pen to be 3 times as long as

it is wide. He plans to use 68 ft of fencing. Find the dimensions of the

pen.

Relate: 2 • width + length = perimeter

Define: Let w = the width.

Then 3w = the length.

Write: 2 w + 3w = 68

1-3


(continued)

5w = 68 Add.

Check: Is the answer reasonable? Since the dimensions are about 14 ft by 41 ft and 14 + 14 + 41 = 69, the perimeter is about 69 ft. The answer is reasonable.

1-3

w = 13 Divide each side by 5.35

3w = 40 Find the length.45

35The width is 13 ft and the length is 40 ft.4

5


The sides of a quadrilateral are in the ratio 1 : 2 : 3 : 6. The

perimeter is 138 cm. Find the lengths of the sides.

Relate: Perimeter equals the sum of the lengths of the four sides.

Define: Let x = the length of the shortest side.

Then 2x = the length of the second side.

Then 3x = the length of the third side.

Then 6x = the length of the fourth side.

1-3


(continued)

Write: 138= x + 2x + 3x + 6x138 = 12xCombine like terms.11.5 = x2x = 2(11.5) 3x = 3(11.5) 6x = 6(11.5) Find the length of

= 23 = 34.5 = 69 each side.

Check: Is the answer reasonable? Since 12 + 23 + 35 + 69 = 139, the answer is reasonable.

The lengths of the sides are 11.5 cm, 23 cm, 34.5 cm, and 69 cm.

1-3


A plane takes off from an airport and flies east at a speed of

350 mi/h. Thirty-five minutes later, a second plane takes off from the

same airport and flies east at a higher altitude at a speed of 400 mi/h.

How long does it take the second plane to overtake the first plane?

1-3

Relate: distance first plane travels = distance second plane travels.

Define: Let t = the time in hours for the second plane.

Then t + = the time in hours for the first plane.3560

Write: 400t = 350 (t + ) 7 12

400t = 350t + Distributive Property 12256


(continued)

50t = Solve for t.12256

1-3

t = 4 h or about 4 h 5 min 1 12

Check: Is the answer reasonable? In 4 h, the second plane travels 1600

mi. In 4 h, the first plane travels about 1600 mi. The answer is

reasonable.

23

Algebra 2 Lesson 1-3 (Page 18) ALGEBRA 2 LESSON 1-3 Solving Equations 1-1.

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