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kati45 [8]
1 year ago
10

Solve the inequality. 3x+6<3(x-7)

Mathematics
2 answers:
GarryVolchara [31]1 year ago
6 0
<h3>\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{3x+6 < 3(x-7) } \end{gathered}$} }</h3>

Simplify both sides of the inequality.

\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{3x+6 < 3x-21 } \end{gathered}$} }

Subtract 3x from both sides.

<h3>\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{3x+6-3x < 3x-21-3x } \end{gathered}$} }</h3><h3>\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{6 < -21 } \end{gathered}$} }</h3>

Subtract 6 from both sides.

<h3>\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{6-6 < -21-6 } \end{gathered}$} }</h3>

\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{0 < -27} \end{gathered}$} }

<h2>There are no solutions.</h2><h3>Standard form: x ∈ ∅</h3>
Mrrafil [7]1 year ago
5 0

Answer:

0 < - 27

Step-by-step explanation:

1. Distribute

3x + 6 < 3(x-7)

3x + 6 < 3x - 21

2. Subtract 6 from both sides

3x + 6 <  3x - 21

3x + 6 - 6 < 3x - 21 - 6

3. Simplify

   subtract

    3x + 6 - 6 < 3x - 21 - 6

    3x <  3x - 21 - 6

   subtract

     3x < 3x - 21 - 6

     3x < 3x - 27

4. Subtract 3x from both sides

3x < 3x - 27

3x - 3x < 3x - 27 - 3x

5. Simplify

    combine like terms

     3x - 3x < 3x - 27 - 3x

     0 < 3x - 27 - 3x

     0 < 3x - 27 - 3x

      0 < -  27

And that is how you get your answer

   

     

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If the Jackson family drive 135 miles on 6 gallons of gas, how many miles can they can they drive on 9 gallons?
drek231 [11]

Answer:

202.5 miles

Step-by-step explanation:

We find the unit rate of the mile per gallon

135/6

= 22.5

We multiply 22.5 by 9 to get the miles they can drive on 9 gallons

22.5 * 9

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3 0
2 years ago
Read 2 more answers
) One year, professional sports players salaries averaged $1.5 million with a standard deviation of $0.9 million. Suppose a samp
Nutka1998 [239]

Answer:

Probability that the average salary of the 400 players exceeded $1.1 million is 0.99999.

Step-by-step explanation:

We are given that one year, professional sports players salaries averaged $1.5 million with a standard deviation of $0.9 million.

Suppose a sample of 400 major league players was taken.

<em>Let </em>\bar X<em> = sample average salary</em>

The z-score probability distribution for sample mean is given by;

                 Z = \frac{ \bar X -\mu}{{\frac{\sigma}{\sqrt{n} } }} }  ~ N(0,1)

where, \mu = mean salary = $1.5 million

            \sigma = standard deviation = $0.9 million

             n = sample of players = 400

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

So, probability that the average salary of the 400 players exceeded $1.1 million is given by = P(\bar X > $1.1 million)

    P(\bar X > $1.1 million) = P( \frac{ \bar X -\mu}{{\frac{\sigma}{\sqrt{n} } }} } >  \frac{ 1.1-1.5}{{\frac{0.9}{\sqrt{400} } }} } ) = P(Z > -8.89) = P(Z < 8.89)

<em>Now, in the z table the maximum value of which probability area is given is for critical value of x = 4.40 as 0.99999. So, we can assume that the above probability also has an area of 0.99999 or nearly close to 1.</em>

Therefore, probability that the average salary of the 400 players exceeded $1.1 million is 0.99999.

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2 years ago
Simplify the following expression:<br> 4x - 3y + 2z - 3x - y + 3z = ?
nordsb [41]
Add all the like terms together so 4x-3x is x or 1x -3y-y is -4y 2z+3z is 5z so put them all together it's x-4y+5z
7 0
3 years ago
Alicia has been putting her money from work into her savings account. The equation f(x)=13x+100 can be used to represent the inc
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Answer:

f(18)=334

Step-by-step explanation:

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