How do you solve the inequality 2x − 3 < −5

Mathematics

1 answer:

larisa86 [58]3 years ago

6 0

Answer:

x=< -1

Step-by-step explanation:

move the constant to the right-hand side and change its sign. 2x<-5+3

Calculate the sum

2x<-2

Divide both sides of the inequality by 2

x <-1

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Soleil and Malvin each work a job. Soleil starts with $700 and makes $100 per day. Malvin starts out with $200 and makes $120 pe

Goshia [24]

Answer:

Soleil and Malvin would have $ 5,000 all together after 13 days.

Step-by-step explanation:

Since Soleil and Malvin each work a job, and Soleil starts with $ 700 and makes $ 100 per day while Malvin starts out with $ 200 and makes $ 120 per day, to determine after how many days will they have at least $ 5000 all together it must be done the following calculation:

5,000 - 700 - 200 = 4,100

200X + 120X = 4,100

320X = 4,100

X = 4,100 / 320

X = 12.8

So Soleil and Malvin would have $ 5,000 all together after 13 days.

5 0

3 years ago

Exercise 2.2.5. Let [[x]] be the greatest integer less than or equal to x. For example, [[π]] = 3 and [[3]] = 3. For each sequen

Debora [2.8K]

Answer:

a) $\lim_{n\rightarrow \infty}a_n=0$

b) The limit is [[4/3]]=1, that is, $\lim_{n\rightarrow \infty}a_n=1$

Step-by-step explanation:

The definition of the limit of a sequence (an) is as follows:

$\lim_{n\rightarrow \infty}a_n=L$ (the sequence (an) converges to L) means that given $\epsilon>0$ , there exists some natural number N such that if n≥N, then $|a_n-L|$

We will use that [[x]] is a increasing function. That is, if x≤y then [[x]]≤[[y]]

a) For all $\epsilon>0$ , take N≥6. Then 1/N ≤1/6 and 5/N ≤ 5/6 < 1. We have that 0<5/N<1, therefore [[5/N]]=0 (0 is the biggest integer less than or equal than x, for any x on the interval 0<x<1)

For n≥N, we have that 1/n ≤ 1/N, hence 0< 5/n ≤ 5/N < 1 . As we discussed above, [[5/n]]=0. Then |a_n|=0, therefore $|a_n-0|=|a_n|=0$