Chapter 3 Section 4: From Words to Algebraic Expressions Answers ...

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Chapter 3 Section 4: From Words to Algebraic Expressions. Answers to Problems . Under each word expression, write the corresponding algebraic expression in ...
Chapter 3 Section 4: From Words to Algebraic Expressions Answers to Problems

Under each word expression, write the corresponding algebraic expression in standard form. 1.

M plus 4

2.

M minus 4

M +4

4.

M times 4

5.

The sum of 9 and 2t

r decreased by 1

8.

6 decreased by 3s

Q subtracted from 18

11.

ab multiplied by −3 −3ab

14.*

B times the sum of 15 and x

B ( 15 + x )

18 − Q

16.

pq multiplied by −4

17.

t more than 6r

−4 pq

19. The product of 2a and 3r

6r + t 20.

s less than 3Y

2a ⋅ 3r or 6ar

3Y − s

22. Nine-fifths of C, plus 32 9 C + 32 5

23.

25. 45 less than 9as

26.

2T divided by L 2T or 2T ÷ L L

s+2 9.

n2 − 7

12. One-fifth of 2R 1 ( 2R) 5 15. The quotient 9 divided by N 9 N 18. Three-fourths of A 3 A 4 21. A sixth part of 2 + y 1 (2 + y) 6

2b 2 − 16

hbw The sum of 2 L and 2 H 2L + 2H

29.

7 fewer than n 2

24. 16 fewer than 2b 2

h times bw

9as − 45 28.

s increased by 2

6 − 3s

t3 + 5

13.

6.

r −1

9 + 2t 10. The total of t 3 and 5

M divided by 4 M 4

M −4

4M

7.

3.

m + n multiplied by 13

13 ( m + n )

*See Explanations & Worked Solutions on page 3.

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27.

b 2 minus 4ac b 2 − 4ac

30. 16 more than −2ax

−2ax + 16

31.

pq added to −5r −5r + pq

32.

−43 multiplied by 2xt −43 ⋅ 2xt

33.

The total of 2 R 3 and 3s 2 2R3 + 3s2

34.

The quotient 2 A + 2 B , divided by C 2 A + 2B C

35.

−3m increased by 2n

36.

4r subtracted from 5MN

Five-sixths of −7 xy

38. The product of −42 A and 3DW

37.

−3m + 2n

5 ⋅ −7 xy 6

40.

−4 less than 8x

2s plus 4c , divided by 5

39.* 3 times x , plus 4

3x + 4

−42 A ⋅ 3 DW 41. 7.5 less than the product of 3a and 2b

8 x − ( −4 ) 43.*

5 MN − 4r

42.

16.4 plus the quotient 8n divided by 4m 8n 16.4 + 4m

45.

E minus m times c 2

3a ⋅ 2b − 7.5 44.

x multiplied by 2x , decreased by 9

2 s + 4c 5

x ⋅ 2x − 9

E − m ⋅ c2

Write an algebraic equation or inequality for each of the following. 46.

3 + m = 24

3 plus m is equal to 24.

47.* 12 less than the product of 4 and a number is equal to 5 times the number. Use x for the variable. 48.

The product of 5 and m + 7 is less than 13.

49.* The quotient of 17 and 2t is equal to the product of 4 and t .

50.

5 ( m + 7 ) < 13 17 = 4t 2t

3 + k > 17 − k

3 plus k is greater than 17 minus k .

51.* The product of 2 and H is less than or equal to H plus 10.

52.*

4 x − 12 = 5 x

T minus 3, divided by 5, is greater than or equal to T plus 4, divided by 7.

*See Explanations & Worked Solutions on page 3.

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2H ≤ H + 10 T −3 T +4 ≥ 5 7

*Explanations & Worked Solutions 14. The word "sum" indicates addition. You need parentheses to indicate that the entire sum is multiplied by B. 39. There is no punctuation so we translate directly: 3x + 4 . 43. The comma indicates a pause, showing that the addition is grouped together:

2 s + 4c . 5

47. First insert parentheses around the phrases: 12 less than (the product of 4 and a number) is equal to (5 times the number). Next translate the phrases enclosed by parentheses into algebraic expressions: 12 less than (4x) = (5x). Now finish it off, dropping the parentheses: 4 x − 12 = 5x . 49. First insert parentheses around the phrases: (The quotient of 17 and 2t ) = (the product of 4 and t ). Next translate the phrases enclosed by parentheses into algebraic expressions:

⎛ 17 ⎞ ⎜ ⎟ = ( 4t ) . ⎝ 2t ⎠ Now finish it off, dropping the parentheses:

17 = 4t . 2t 51. First insert parentheses around the phrases: (The product of 2 and H ) ≤ ( H plus 10). Next translate the phrases enclosed by parentheses into algebraic expressions: ( 2 H ) ≤ ( H + 1 0) . Now finish it off, dropping the parentheses: 2H ≤ H + 10 . 52. First insert parentheses around the phrases: ( T minus 3) divided by 5 ≥ ( T plus 4) divided by 7. Next translate the phrases enclosed by parentheses into algebraic expressions: (T − 3) divided by 5 ≥ (T + 4 ) divided by 7. Now finish it off, dropping the parentheses:

T −3 T +4 ≥ 5 7

.

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