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2 years ago

What is the solution to the inequality 7x + 2 < -3x + 1?

Mathematics

1 answer:

anastassius [24]2 years ago

5 0

Answer:

$\Large\boxed{\sf{x < -\dfrac{1}{10} }}$

Step-by-step explanation:

In order to find the solutions, you must isolate the inequality on one side of the equation.

7x+2<-3x+1

First, you subtract by 2 from both sides.

7x+2-2<-3x+1-2

Solve.

Subtract the numbers from left to right.

7x<-3x-1

Add by 3x from both sides.

7x+3x<-3x-1+3x

Solve.

7x+3x=10x

10x<-1

Then, you divide by 10 from both sides.

10x/10<-1/10

Solve.

Divide these numbers goes from left to right.

$\Longrightarrow: \boxed{\sf{x < -\dfrac{1}{10} }}$

Therefore, the final answer is x<-1/10.

I hope this helps, let me know if you have any questions.

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AleksandrR [38]

Answer:

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3 years ago

How else can the ratio 4⁄5 be written? A. .2 B. 5⁄4 C. 5:4 D. 4:5

Y_Kistochka [10]

$\frac{x}{y}$ will be either x to y or x : y
so,
$\frac{4}{5}$ will be 4 :5

Answer is: D. 4 : 5

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3 years ago

Read 2 more answers

The ratio of angle measures is 1:2:2. Classify the triangle by its angle measures. obtuse triangle right triangle equiangular tr

lyudmila [28]

Answer:

Acute Triangle

Step-by-step explanation:

Angles in a triangle add up to 180 degrees.

So,

x+2x+2x = 180

=> 5x = 180

Dividing both sides by 5

=> x = 36

So, The lengths are:

=> 36

=> 72

Since all the angles are less than 90 degrees, It is an acute triangle.

5 0

4 years ago

A new battery's voltage may be acceptable (A) or unacceptable (U). A certain flashlight requires two batteries, so batteries wil

klio [65]

Answer:

The probability that you test exactly 4 batteries is 0.0243.

Step-by-step explanation:

We are given that a new battery's voltage may be acceptable (A) or unacceptable (U). A certain flashlight requires two batteries, so batteries will be independently selected and tested until two acceptable ones have been found.

Suppose that 90% of all batteries have acceptable voltages.

Let the probability that batteries have acceptable voltages = P(A) = 0.90

So, the probability that batteries have unacceptable voltages = P(U) = 1 - P(A) = 1 - 0.90 = 0.10

Now, the probability that you test exactly 4 batteries is given by the three cases. Firstly, note that batteries will be tested until two acceptable ones have been found.

So, the cases are = P(AUUA) + P(UAUA) + P(UUAA)

This means that we have tested 4 batteries until we get two acceptable batteries.

So, required probability = (0.90 $\times$ 0.10 $\times$ 0.10 $\times$ 0.90) + (0.10 $\times$ 0.90 $\times$ 0.10 $\times$ 0.90) + (0.10 $\times$ 0.10 $\times$ 0.90 $\times$ 0.90)

= 0.0081 + 0.0081 + 0.0081 = 0.0243

Hence, the probability that you test exactly 4 batteries is 0.0243.

3 0

3 years ago

Julio is ordering books from BestBooks for his reading club. The table shows Julio's total cost of the book order, Including the

timama [110]

Answer:

Shipping Fee = $ 6

Step-by-step explanation:

The complete question and the table is as follows :

Given - Julio is ordering books from Best Books for his reading club. The table shows Julio's total cost of the book order, Including the shipping fee for each order. Best Books charges the same shipping fee for every book order.

To find - How much is the shipping fee?

Proof -

We know that,

Total Cost = (Number of books buy)(Cost of 1 book) + Shipping Fee

Let us Assume that,

Cost of 1 book = x

Shipping Fee = y

So,

From the table, we get

21 = 5x + y ..........(1)

36 = 10x + y ..........(2)

51 = 15x + y ..........(3)

66 = 20x + y ..........(4)

From equation (1), we get

y = 21 - 5x

Put the value of y in equation (2), we get

36 = 10x + 21 - 5x

⇒36 = 5x + 21

⇒5x = 36 - 21

⇒5x = 15

⇒x = $\frac{15}{5}$ = 3

∴ we get

x = 3

Put the value of x , we get

y = 21 - 5(3)

= 21 - 15

= 6

⇒y = 6

SO, we get

x = 3

y = 6

Verify the 4 Equations :

21 = 5x + y ..........(1)

21 = 5(3) + 6

= 15 + 6

= 21

⇒21 = 21

Verified

36 = 10x + y ..........(2)

36 = 10(3) + 6

= 30 + 6

= 36

⇒36 = 36

Verified

51 = 15x + y ..........(3)

51 = 15(3) + 6

= 45 + 6

= 51

⇒51 = 51

Verified

66 = 20x + y ..........(4)

66 = 20(3) + 6

= 60 + 6

= 66

⇒66 = 66

Verified

So, we get

Cost of 1 book = x = $ 3

Shipping Fee = y = $ 6

7 0

3 years ago