Algebra 2 Lesson 1-3 (Page 18) ALGEBRA 2 LESSON 1-3 Solving Equations 1-1.
-
Upload
bathsheba-simmons -
Category
Documents
-
view
221 -
download
2
Transcript of 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.
ALGEBRA 2 LESSON 1-3ALGEBRA 2 LESSON 1-3
Solving EquationsSolving Equations
1-1
New Vocabulary
ALGEBRA 2 LESSON 1-3ALGEBRA 2 LESSON 1-3
Solving EquationsSolving Equations
1-1
A number that makes the equation true is a
solution of the equation.
Properties of Equality (Page 18)
ALGEBRA 2 LESSON 1-3ALGEBRA 2 LESSON 1-3
Solving EquationsSolving Equations
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
Solving EquationsSolving EquationsALGEBRA 2 LESSON 1-3ALGEBRA 2 LESSON 1-3
Try this one on your own. Check your answer.
1-3
215128 zz
Solving EquationsSolving EquationsALGEBRA 2 LESSON 1-3ALGEBRA 2 LESSON 1-3
Try this one on your own. Check your answer.
1-3
tt 4932
Solving EquationsSolving EquationsALGEBRA 2 LESSON 1-3ALGEBRA 2 LESSON 1-3
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.
1-3
m = – Divide each side by 7.247
Solving EquationsSolving EquationsALGEBRA 2 LESSON 1-3ALGEBRA 2 LESSON 1-3
Try this one on your own. Check your answer.
1-3
706)3(2 y
Solving EquationsSolving EquationsALGEBRA 2 LESSON 1-3ALGEBRA 2 LESSON 1-3
Try this one on your own. Check your answer.
1-3
)29(26)2(6 tt
Solving EquationsSolving EquationsALGEBRA 2 LESSON 1-3ALGEBRA 2 LESSON 1-3
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
Solving EquationsSolving EquationsALGEBRA 2 LESSON 1-3ALGEBRA 2 LESSON 1-3
Try this one on your own. Check your answer.
1-3
1
21
for equation theSolve2
1 : is trapezoida of areafor formula The
b
bbhA
Solving EquationsSolving EquationsALGEBRA 2 LESSON 1-3ALGEBRA 2 LESSON 1-3
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.
Solving EquationsSolving EquationsALGEBRA 2 LESSON 1-3ALGEBRA 2 LESSON 1-3
Try this one on your own. Check your answer.
1-3
.for 015equation theSolve xbxax
Solving EquationsSolving EquationsALGEBRA 2 LESSON 1-3ALGEBRA 2 LESSON 1-3
Try this one on your own. Check your answer.
1-3
.for 2
equation theSolve xba
xd
To solve problems by writing equations.
ALGEBRA 2 LESSON 1-3ALGEBRA 2 LESSON 1-3
Solving EquationsSolving Equations
1-1
Solving EquationsSolving EquationsALGEBRA 2 LESSON 1-3ALGEBRA 2 LESSON 1-3
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
Solving EquationsSolving EquationsALGEBRA 2 LESSON 1-3ALGEBRA 2 LESSON 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
Solving EquationsSolving EquationsALGEBRA 2 LESSON 1-3ALGEBRA 2 LESSON 1-3
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
Solving EquationsSolving EquationsALGEBRA 2 LESSON 1-3ALGEBRA 2 LESSON 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
Solving EquationsSolving EquationsALGEBRA 2 LESSON 1-3ALGEBRA 2 LESSON 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
Solving EquationsSolving EquationsALGEBRA 2 LESSON 1-3ALGEBRA 2 LESSON 1-3
(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