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Vadim26 [7]
4 years ago
14

Solve for b. Give an exact answer in simplified form. -67b + 6 < 9b + 43

Mathematics
2 answers:
prohojiy [21]4 years ago
4 0

it equals b 37 58 it welcome

Kisachek [45]4 years ago
4 0

Answer:

b≥−  37/76

​  

Step-by-step explanation:

\begin{aligned}-67b+6 & \leq 9b + 43 \\\\ -67b&\leq 9b+37 &(\text{Subtract } 6 \text{ from both sides}) \\\\ -76b &\leq 37 &(\text{Subtract } 9b \text{ from both sides})\\\\ 76b&\geq -37&(\text{Multiply both sides by }-1)\\\\ b&\geq-\dfrac{37}{76}&(\text{Divide both sides by }76) \end{aligned}  

−67b+6

−67b

−76b

76b

b

​  

 

≤9b+43

≤9b+37

≤37

≥−37

≥−  

76

37

​  

 

​  

 

(Subtract 6 from both sides)

(Subtract 9b from both sides)

(Multiply both sides by −1)

(Divide both sides by 76)

​

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2. Which of the following are terms of the series with nth term T-3n +17? a) 80 b) 170 c)217 d) 312 e) 278 f) 3566
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Answer:

The correct options are a,b,e and f.

Step-by-step explanation:

It is given that the nth terms of the series is defined as

T_n=3n+17

Subtract 17 from both the sides.

T_n-17=3n

Divide both sides by 3.

\frac{T_n-17}{3}=n

The term Tₙ is a term of given series if n is a positive integer.

(a) The given term is 80.

n=\frac{80-17}{3}=21

Since n is a positive integer, therefore 80 is a term of given series.

(b) The given term is 170.

n=\frac{170-17}{3}=51

Since n is a positive integer, therefore 170 is a term of given series.

(c) The given term is 217.

n=\frac{217-17}{3}=66.67

Since n is not a positive integer, therefore 217 is a term of given series.

(d) The given term is 312.

n=\frac{312-17}{3}=98.33

Since n is not a positive integer, therefore 312 is a term of given series.

(e) The given term is 278.

n=\frac{278-17}{3}=87

Since n is a positive integer, therefore 278 is a term of given series.

(f) The given term is 3566.

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Since n is a positive integer, therefore 3566 is a term of given series.

Thus, the correct options are a, b, e and f.

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3 years ago
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