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:
