algebra 1 lesson 10-2 (for help, go to lessons 1-4, 1-5, and 2-1.) complete each statement with....

ALGEBRA 1 LESSON 10-2ALGEBRA 1 LESSON 10-2

(For help, go to Lessons 1-4, 1-5, and 2-1.)

Complete each statement with <, =, or >.

1. –3 + 4 –5 + 4

2. –3 – 6 4 + 6

3. –3.4 + 2 –3.45 + 2

Solve each equation.

4. x – 4 = 5 5. n – 3 = –5

6. t + 4 = –5 7. k + = 23

56

Solving Inequalities Using Addition and Subtraction

10-2


1. –3 + 4 –5 + 4

1 > –1

2. –3 – 6 4 – 6

–9 < –2

3. –3.4 + 2 –3.45 + 2

–1.4 > –1.45

4. x – 4 = 5x = 9

5. n – 3 = –5n = –2

6. t + 4 = –5t = –9

Solutions


10-2

7. k + =

k = – = – =

23

56

23

56

56

46

16


Solve p – 4 < 1. Graph the solutions.

p – 4 + 4 < 1 + 4 Add 4 to each side.

p < 5 Simplify.


10-2


Solve 8 d – 2. Graph and check your solution.>

8 + 2 d – 2 + 2 Add 2 to each side.>

10 d, or d 10 Simplify.> <

Check: 8 = d – 2 Check the computation.8 10 – 2 Substitute 10 for d.8 = 88 d – 2 Check the direction of the inequality.8 9 – 2 Substitute 9 for d.8 7

>>>


10-2


Solve c + 4 > 7. Graph the solutions.

c + 4 – 4 > 7 – 4 Subtract 4 from each side.

c > 3 Simplify.


10-2


In order to receive a B in your literature class, you must earn more than 350 points of reading credits. Last week you earned 120 points. This week you earned 90 points. How many more points must you earn to receive a B?


10-2

points pointsearned required

points needed

Relate: plusis more

than

Define: Let = the number of points needed.p

Write: 120 + 90+ 350p >


(continued)

You must earn 141 more points.

210 + p > 350 Combine like terms.

120 + 90 + p > 350

210 + p – 210 > 350 – 210 Subtract 210 from each side.

p > 140 Simplify.


10-2


Solve each inequality. Graph the solutions.

1. p – 7 –5 2. w – 3 < –9

3. x + 6 > 4 4. 13 9 + h

>

>

p 2> w < –6

x > –2 <4 h, or h 4>


10-2

(For help, go to Lessons 2-1 and 3-1.)


Solve each equation.

1. 8 = t 2. 14 = –21x 3. = –1

4. 5d = 32 5. x = –12 6. 0.5n = 9

Write an inequality for each graph.

7. 8.

12

x6

23

Solving Inequalities Using Multiplication and Division

10-2


Solutions

1. 8 = t

t = 8

t = 8(2) = 16

12

12

2. 14 = –21x

–21x = 14

x = – = –1421

23

3. = –1

x = –1(6) = –6

x6 4. 5d = 32

d = = 6.4325

5. x = –12

• x = • –12

x = –18

32

23

23

32

6. 0.5n = 9

=

n = 18

0.5n0.5

90.5

7. x –1 8. x > 3<


10-2


Solve > –2. Graph and check the solutions.z3

z > –6 Simplify each side.

3 > 3(–2) Multiply each side by 3. Do not reverse the inequality symbol.

z3( )

z3 > –2 Check the direction of the inequality.

Check: = –2 Check the computation.z3

– = –2 Substitute –6 for z.63

–2 = –2 Simplify.

– > –2 Substitute –3 for z.33

–1 > –2 Simplify.


10-2


Solve 3 – x. Graph and check the solutions.< 35

( )53–( )5

3– (3) > ( )35

xMultiply each side by the reciprocal of – , which

is – , and reverse the inequality symbol.

35

53

–5 x, or x –5 Simplify.<>


10-2


(continued)

Check: 3 = – x Check the computation.

3 = – (–5) Substitute –5 for x.

3 = 3

3 – x Check the direction of the inequality.

3 – (–10) Substitute –10 for x.

3 6

35

35

<

<

<

35

35


10-2


Solve –4c < 24. Graph the solutions.

c > –6 Simplify.

Divide each side by –4. Reverse the inequality symbol.–4c–4 >

24–4


10-2


Your family budgets $160 to spend on fuel for a trip. How many times can they fill the car’s gas tank if it cost $25 each time?

Your family can fill the car’s tank at most 6 times.

cost per total fueltank budget

Relate: timesnumberof tanks

is atmost

Define: Let = the number of tanks of gas.t

Write: 25 • 160t <

25t 160<


10-2

Divide each side by 25.<25t25

16025

t 6.4 Simplify.<


Solve each inequality. Graph the solution.

1. –3

2. – < –1

3. 6x < 30

4. 48 –12h

y2 >

p3

>

y –6>

p > 3

x < 5

><–4 h, or h –4


10-2


(For help, go to Lessons 2-2 and 2-3.)

Solve each equation, if possible. If the equation is an identity or if it has no

solution, write identity or no solution.

1. 3(c + 4) = 6 2. 3t + 6 = 3(t – 2)

3. 5p + 9 = 2p – 1 4. 7n + 4 – 5n = 2(n + 2)

5. k – + k = 6. 2t – 32 = 5t + 1

Find the missing dimension of each rectangle.

7. 8.

12

23

76

Solving Multi-Step Inequalities

10-2


1. 3(c + 4) = 6 2. 3t + 6 = 3(t – 2)

c + 4 = 2 3t + 6 = 3t – 6

c = –2 6 = –6

no solution

3. 5p + 9 = 2p – 1 4. 7n + 4 – 5n = 2(n + 2)

3p = –10 2n + 4 = 2n + 4

p = –3 identity13

Solving Multi-Step InequalitiesSolutions

10-2


5. k – + k = 6. 2t – 32 = 5t + 1

k = –3t = 33

k = = 1 t = –11

7. P = 2( + w) 8. P = 2( + w)

110 = 2( + 15) 78 = 2(26 + w)

55 = + 15 39 = 26 + w

40 = 13 = w

length = 40 cm width = 13 in.

12

23

76

32

116

116

29

Solutions


10-2


Solve 5 + 4b < 21.

5 + 4b – 5 < 21 – 5 Subtract 5 from each side.

4b < 16 Simplify.

b < 4 Simplify.

< Divide each side by 4.4b4

164

Check: 5 + 4b = 21 Check the computation.

5 + 4b < 21 Check the direction of the inequality.

5 + 4(3) < 21 Substitute 3 for b.

5 + 4(4) 21 Substitute 4 for b.

21 = 21

17 < 21


10-2


The band is making a rectangular banner that is 20 feet long

with trim around the edges. What are the possible widths the banner

can be if there is no more than 48 feet of trim?

twice the the lengthlength of trim

Relate: plustwice the

widthcan be nomore than

Write: 2(20) + 2w 48<


10-2


(continued)

The banner’s width must be 4 feet or less.

2(20) + 2w 48<

40 + 2w 48 Simplify 2(20).<

40 + 2w – 40 48 – 40 Subtract 40 from each side.<

2w 8 Simplify.<

w 4 Simplify.<

Divide each side by 2.<2w2

82


10-2


Solve 3x + 4(6 – x) < 2.

3x + 24 – 4x < 2 Use the Distributive Property.

–x + 24 < 2 Combine like terms.

–x + 24 – 24 < 2 – 24 Subtract 24 from each side.

–x < –22 Simplify.

x > 22 Simplify.

> Divide each side by –1. Reverse the inequality symbol.

–x–1

–22–1


10-2

Solve 8z – 6 < 3z + 12.


8z – 6 – 3z < 3z + 12 – 3z Subtract 3z from each side.

5z – 6 < 12 Combine like terms.

5z – 6 + 6 < 12 + 6 Add 6 to each side.

5z < 18 Simplify.

< Divide each side by 5.5z5

185

z < 3 Simplify.35


10-2


Solve 5(–3 + d) 3(3d – 2).<

–15 – 4d + 15 –6 + 15 Add 15 to each side. <

–4d 9 Simplify.<

–15 + 5d – 9d 9d – 6 – 9d Subtract 9d from each side. <

–15 – 4d –6 Combine like terms.<

–15 + 5d 9d – 6 Use the Distributive Property.<

Divide each side by –4. Reverse the inequality symbol.

–4d–4

9 –4>

d –2 Simplify.>14


10-2


Solve each inequality.

1. 8 + 5a 23 2. – p < p – 6

3. 3(x – 4) > 4x + 7 4. 3(3c + 2) 2(3c – 2)

>

<

13

12

a 3> p > 7 15

x < –19 <c –313


10-2

algebra 1 lesson 10-2 (for help, go to lessons 1-4, 1-5, and 2-1.) complete each statement with....

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