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kow [346]
3 years ago
5

Solve -7 < 3x + 2 < 14

Mathematics
2 answers:
zepelin [54]3 years ago
5 0

Answer:

- 7 < (3x + 2) < 14 \\  \\ =  \:  \:   - 7 - 2 < 3x < 14 - 2 \\  \\ =  \:  \:   - 9 < 3x < 12 \\  \\  =  \:  \:  \frac{ - 9}{3}  <  \frac{3x}{3}  <  \frac{12}{3}  \\  \\  = { \boxed{ \boxed{ - 3 < x < 4}}}

ratelena [41]3 years ago
4 0

Answer:

-3<x<4

Step-by-step explanation:

Hi there!

We are given the double inequality -7<3x+2<14 and we want to solve it.

If we have a double inequality and we want to do something (like subtract 3), then we must subtract 3 from the left side, middle, and right side.

An example would be with the inequality 1<x+3<5

In order to isolate x, we'll subtract 3 from the center. However, we'll also be needing to subtract 3 from the left (1-3) and the right (5-3)

Hence,

1<x+3<5

-3   -3  -3

___________

-2<x<2

In our problem then, we'll be subtracting 2 from EVERY side.

-7<3x+2<14

-2      -2   -2

________________

-9 < 3x  < 12

Now in order to isolate x, we'll divide by 3, which once again, we divide on EVERY side

-3<x<4

Hope this helps!

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Five distinct numbers are randomly distributed to players numbers 1 through 5. Whenever two playerscompare their numbers, the on
ad-work [718]

Answer:

Observe that the first and the second player have equal probability to get any of number. Using the principle of that symmetry, we have that  

P(X=0)=\frac{1}{2}

<u>Event X = 1 </u>means that the first player has got greater number than the second player, but not than the third player. So, choose any three numbers out of five of them and say that the minimal number out of these three goes to the second player, mean number to the first one and the largest to the third one. Permute remaining two numbers on remaining two people. Hence

P(X=1)=\frac{1}{6}

<u>Event X = 2</u> means that the first player has got greater number than the second and the third player, but not than the fourth player. So, choose any four numbers out of five of them and say that the minimal number and the next minimal out of these four go to the second and the third player (and permute them), third number to the first one and the largest to the fourth player. Give remaining number to the last person. Hence

P(X=2)=\frac{1}{12}

<u>Event X = 3</u> means that the first player has got greater number than the second, the third, and the forth player, but not than the fifth player. So, permute these five numbers as follows: give the highest to the last person, the second highest to the first, and permute remaining numbers on the remaining people. Hence  

P(X=3)=\frac{1}{20}

<u>Event X = 4</u> means basically the first player has won all the battles i.e, he has got the greatest number. Hence

P(X=4)=\frac{1}{5}

7 0
3 years ago
What is 3n-2/5=7/10 solve please
Tems11 [23]

Answer:  \bold{n=\dfrac{11}{6}}

<u>Step-by-step explanation:</u>

\dfrac{3n-2}{5}=\dfrac{7}{10}\\\\\\10(3n-2)=5(7)\qquad \longrightarrow \quad \text{(cross multiplied)}\\\\30n-20=35\qquad \longrightarrow \quad \text{(distributed)}\\\\30n=55\qquad \longrightarrow \quad \text{(added 20 to both sides)}\\\\n=\dfrac{55}{30}\qquad \longrightarrow \quad \text{(divided 30 from both sides)}\\\\n=\dfrac{11}{6}\quad \longrightarrow \quad \text{(simplified fraction)}\\\\\\\large\boxed{n=\dfrac{11}{6}}\\

8 0
3 years ago
Please help me answer these questions asap!!
vekshin1
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8 0
2 years ago
Write a trinomial expression that is equivalent to (2x+5)(3x-2)
Vikentia [17]
2x *3x =6x^2

2x*(-2)= -4x

5*3x=15x

5* (-2) =- 10

6x^2 -4x +15x -10

6x^2 + 11x -10
7 0
2 years ago
Use substitution to solve each system of equations.<br> y = 5x -2<br> 3 x- 5y =4
Nezavi [6.7K]
  • x = 3/11
  • y = -7/11

Step-by-step explanation:

y = 5x - 2…Equation 1

3x - 5y = 4…Equation 2

Subtitute value of y to Equation 2 :

3x - 5(5x - 2) = 4

3x - 25x + 10 = 4

-22x + 10 = 4

10 - 4 = 22x

6 = 22x

6/22 = x

<u>3/11 = </u><u>x</u>

Subtitute value of x to one of Equation :

for example Equation 2…

3x - 5y = 4

3(3/11) - 5y = 4

9/11 - 5y = 4

9/11 - 4 = 5y

(9 - 44)/11 = 5y

(-35)/11 = 5y

(-35)/11 × 1/5 = y

<u>-7/11 = y</u>

7 0
2 years ago
Read 2 more answers
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