Solve the equation -6+3×=-9


Answer 1
Answer: -6 + 3x = -9

And 6 to both sides:
3x = -3

Divide by 3 on both sides:
x = -1

Answer: x = -1

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The weather in a certain locale consists of alternating wet and dry spells. Suppose that the number of days in each rainy spell is a Poisson distribution with mean 2, and that a dry spell follows a geometric distribution with mean 7. Assume that the successive durations of rainy and dry spells are independent. What is the long-run fraction of time that it rains?




Step-by-step explanation:

The Poisson’s distribution is a discrete probability distribution. A discrete probability distribution means that the events occur with a constant mean rate and independently of each other. It is used to signify the chance (probability) of a given number of events occurring in a fixed interval of time or space.

In the long run, fraction of time that it rains = E(Number of days in rainy spell) / {E(Number of days in a rainy spell) + E(Number of days in a dry spell)}

E(Number of days in rainy spell) = 2

E(Number of days in a dry spell) = 7

In the long run, fraction of time that it rains = 2/(2 + 7) = 2/9

Final answer:

Given the parameters of the rainy spell and dry spell, the long-run fraction of time that it rains can be calculated by dividing the mean of the rainy days by the sum of the average rainy and dry days. Hence, it rains roughly 22.22% of the time in the long-term.


The question is asking about the long-run fraction of time that it rains, based on a rainy spell following a Poisson distribution with a mean of 2 days, and a dry spell following a geometric distribution with an average of 7 days, with the sequences being independent.

We are being asked to calculate the proportion of time that it rains in the long-run, given these distribution parameters. The Poisson and geometric distributions are often used in this type of probability assessment.

To tackle this, we need to divide the mean of the rainy days by the sum of the average rainy and dry days. Thus, the long-run fraction of time it rains is given by 2/(2+7) = 2/9.

So, in the long run, it rains roughly 22.22% (or 2/9) of the time.

Learn more about Probability Distributions here:


Tyson and Ariana each invested $2,500 in separate accounts. Tyson’s interest rate is 5.75% and is compounded annually. Ariana’s simple interest rate is 5.75%. Neither will make any additional deposits or withdrawals. At the end of 6 years, how much more has Tyson earned? Round your answer to the nearest cent.



Tyson's account will have $ 133.90 more than Ariana's account.

Step-by-step explanation:

In Tyson's case, he invests $ 2,500 in an account whose interest rate is 5.75% and is compounded annually. In turn, Ariana invests the same amount and for the same interest, but this is not compounded.

Thus, Ariana, at the end of her 6 years, will have a total amount in her account of $ 3,362.5 (((2,500 x 5.75 / 100) x 6) + 2,500), of which $ 862.5 will correspond to the interest generated.

Instead, Tyson's investment interests will be consolidated annually. Thus, in 6 years, this investment will evolve as follows:

-Year 1 --- 2,500 x 1.0575 = 2,643.75

-Year 2 --- 2,643.75 x 1.0575 = 2,795.76

-Year 3 --- 2,795.76 x 1.0575 = 2,956.52

-Year 4 --- 2,956.52 x 1.0575 = 3,126.52

-Year 5 --- 3,126.52 x 1.0575 = 3,306.29

-Year 6 --- 3,306.29 x 1.0575 = 3,496.40

Thus, at the end of the 6 years, Tyson will have $ 3,496.40 in his account. Thus, Tyson's account will have $ 133.90 more than Ariana's account.

During the soccer season, Cathy made 27 of the 54 goals she attempted. Karla made 18 of the 45 goals she attempted. Patty made 34% of the goals she attempted. List the athletes in order of their goal-scoring percentage from least to greatest.



  Patty, Karla, Cathy

Step-by-step explanation:

The scoring percentage of goals attempted can be computed by dividinggoals made by those attempted, then multiplying the result by 100%.


Cathy's rate is ...

  27/54 × 100% = 50%

Karla's rate is ...

  18/45 × 100% = 40%

Patty's rate is ...

  given as 34%


By least to greatest scoring rate, the athletes are ...

  Patty (34%), Karla (40%), Cathy (50%)

European car company advertises that theircar gers 9.4 Kilometers per liter of gasoline. Convert
this figure to miles per galllon



22.11 miles per gallon

Step-by-step explanation:

1 km = 0.621371 miles

1 litre = 0. 264172 gallon


Mileage of car =  9.4 Milometers per liter of gasoline

Mileage of car = 9.4 Km/ litres

now we will use 0.621371 miles for Km and 0. 264172 gallon for litres

Mileage of car = 9.4 * 0.621371 miles/ 0. 264172 gallon

Mileage of car = 9.4 * 2.3521 miles/ gallon

Mileage of car = 22.11  miles/ gallon

Thus, 9.4 Km/litres is same as 22.11 miles per gallon.

The​ point-slope form of the equation of a nonvertical line with slope, m, that passes through the point (x1,y1) is...?a. Ax+By=c

b. y-y1=m(x-x1)

c. y1=mx1+b

d. Ax1+by1=C

e. y=mx+b

f. y1-y=m(x-x1)

Please explain why, if you can. Thanks! :)


The equation of the line, in point-slope form, is given by:

y - y_1 = m(x - x_1)

Option b.


The equation of a line, in point-slope form, is given by:

y - y_1 = m(x - x_1)

In which

  • m is the slope.
  • The point is (x_1,y_1).
  • Nonvertical line means that m \neq 0
  • Thus, the correct option is given by option b.

A similar problem is given at


  b. y-y1 = m(x-x1)

Step-by-step explanation:

It's a matter of definition. There are perhaps a dozen useful forms of equations for a line. Each has its own name (and use). Here are some of them.

  • slope-intercept form: y = mx + b
  • point-slope form: y -y1 = m(x -x1)
  • two-point form: y = (y2-y1)/(x2-x1)(x -x1) +y1
  • intercept form: x/a +y/b = 1
  • standard form: ax +by = c
  • general form: ax +by +c = 0

Adding y1 to the point-slope form puts it in an alternate form that is useful for getting to slope-intercept form faster: y = m(x -x1) +y1. I use this when asked to write the equation of a line with given slope through a point, with the result in slope-intercept form.

Which inequality's solution is graphed here? A) 3x + 5 > 3 Eliminate B) 3x - 5 > 3 C) 5x + 3 > 3 D) 5x - 3 > 3


The equation of line passing through points (-4, 1) and (2, 3) will be

3y = x + 7

What is the general equation of a Straight line inequality?

An inequality in mathematics compares two values or expressions, showing if one is less than, greater than, or simply not equal to another value. The general equation of a straight line inequality is -

[y] < [m]x + [c]

[y] > [m]x + [c]

[y] ≥ [m]x + [c]

[y] ≤ [m]x + [c]

where -

[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.

The equation of a straight lineinequality can be also written as -

Ax + By + C > 0

By > - Ax - C

y > (- A/B)x - (C/A)

Given is inequality's solution graphed [Refer to graph attached].

The inequality whose solution is graphed is -

5x + 3 > 3

On solving -

5x + 3 > 3

5x + 3 - 3 > 3 - 3

5x > 0

x > 0

Therefore, the inequality whose solution is graphed is

5x + 3 > 3

(Refer the image attached, for reference)

To solve more questions on inequalities, visit the link below -


Here is the graph 
The Answer is C) 5x + 3 > 3