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For example,    abs(-3)

2x + 5  =  3

                                    Subtract  5  from both sides of the equation.

2x + 5 - 5  =  3 - 5

                                    2x + 5 - 5 = 2x   and   3 - 5 = -2

2x  =  -2

                                    Divide both sides of the equation by  2 .

2x/2  =  -2/2

                                    2x/2 = x     and     -2/2 = -1

x  =  -1

You can plug this back into the original equation to see if it is true.

2(-1) + 5  =  3   ?

-2 + 5  =  3      This is true.

Is this your question?     \(\frac3v-\frac8{13}\)

Or is it     \(\sqrt[3]{-\frac{8}{13}}\)

or something else??  

    24[ -(3x² - 4) / 8  +  (-3x² + 4) / 3  -  (-6x² + 7) / 12 ]        Distribute the  24 .

=  -24(3x² - 4) / 8  +  24(-3x² + 4) / 3  -  24(-6x² + 7) / 12     Reduce.

=  -3(3x² - 4)  +  8(-3x² + 4)  -  2(-6x² + 7)          Distribute the number outside each parenthesees.

=  -9x² + 12  +  -24x² + 32  -  -12x² - 14          

=  -9x² + 12  -  24x² + 32  +  12x² - 14              Combine like terms.

=  -21x² + 12 + 32 - 14

=  -21x² + 30

-(3)/(4)(2 - 2x)^(2)          Expand  (2 - 2x)² .

=  -(3)/(4)(2 - 2x)(2 - 2x)

=  -(3)/(4)(4 - 8x + 4x²)

=  -(3)/(4)(4 - 8x + 4x²)        Distribute the  3/4 .

=  -[ (3/4)(4) - (3/4)(8x) + (3/4)(4x²) ]

=  -[ 3 - 6x + 3x² ]

=  -3 + 6x - 3x²

=  -3x² + 6x - 3

Let the distance between Alice and Carla's house =D
Time=Distance / Speed
D/12 + D/36 =1, solve for D
D = 9 miles the distance between the 2 houses.

Let the time she travels at 12 mph  = x minutes and if she trqvels back at 36 mph.....since this is 3 times as fast...it must take her x / 3 minutes  to return

So

x +  x/3  =  60     mutiply through by 3

3x + x  =  180

4x  = 180   divide by 4

45  = x

So....she travels   45/3 minutes = 15 minutes at 36 mph

And since  15 minutes = 1/4 hr......the distance is

Rate x Time  =  36mph  x 1/4 hr  =  9 miles

2x(10 + 5)   =   2x( 15 )   =   2 * x * 15   =   2 * 15 * x   =   30 * x   =   30x

A man attempts to call his math professor. When they do not pick up, he hears their voicemail: 

"The number you have dialed is imaginary. Please, rotate your phone by ninety degrees and try again".

Why didn't the sine cross the road? Cosecant.

8x - 10y  =  -8

y  =  8

Look at the first equation.

8x - 10y  =  -8         Now, since  y = 8 , we can replace  " y "  in this equation with  " 8 " .

8x - 10(8)  =  -8

                               And 10(8) = 80 .

8x - 80  =  -8

                               Add  80  to both sides of the equation.

8x  =  -8 + 80

8x  =  72

                               Divide both sides of the equation by  8 .

x  =  72/8

x  =  9

So the solutions are   x = 9   and   y = 8 .

HAHAHA!!!!!......you guys/girls are too much....!!!!!

One more

Prove that

 sin  x

______   =   6         [ cancel the n's   and we have ]

     n 

si  x      =    6

I found this

I think you want the slope-intercept form for the equation of a line that passes through these points.

slope intercept form is:     y = mx + b     , where  " m "  is the slope and  " b"  is the y-intercept.

slope  =  \(\frac{\text{change in y}}{\text{change in x}}\,=\,\frac{y_2-y_1}{x_2-x_1}\,=\,\frac{-2-(-1)}{3-0}\,=\,\frac{-2+1}{3}\,=\,-\frac13\)

→    m  =  - \(\frac13\)

Since  (0, -1)  is a point on the line, we know that when  x = 0 ,  y = -1  .   So...

the y-intercept  =  -1

→    b  =  -1

So our equation is

y  =  - \(\frac13\)x  - 1

Thanks!

-1 / 3

654 - (- 467 )  =  $1121

Desomos uses a little different notation.....here is the greatest integer function :

https://www.desmos.com/calculator/x7m8hhcrx6

Here's 1

We don't need much math here.....if 5 members paint the wall in 27 minutes.....3 times as many workers - 15 -  must take 1/3 as long  = 9 minutes

Here's 2

8 workers  -  5000 sq ft   -   30 minutes

Here's the way I like to think of these.......in one minute....the 8 workers would paint 

5000/ 30  =  500/3 sq ft...so....to paint 8000 sq ft would take   (8000) / (500/3)  =

8000 * 3 / 500  =    48 minutes

Here's the last one : 

Using the same approach as 2...we have

12 -  2400   - 45

In 1 minute, the 12 members paint  2400/45  = 160/3 sq ft

So...1 worker can paint (1/12)  of this  = ( 160/3 ) (1/12)  = 160 / 36 sq ft

So....in 1 minute  9 workers can paint 9 times as much  =  9 * 160 / 36  =  40 sq ft

So....it will take 9 workers    3600 / 40   =  90 minutes to paint 3600 sq ft

For number 1, we can use what I call the "see-saw" principle

12 * 20   =    N * 15   divide both sides by 15

12 * 20  / 15  =  N  =  240 / 15  =  16  is the number needed

Here's  number two

P  = k H^2      where P is the pounds of gold needrd..k is the proportionality constant and H is the height...we need to find "k"

80  = k * 20^2

80 = k *  400      divide both sides by 400

1/5  = k

So..one that is 25 feet tall requires

P =  (1/5) * 25^2 =    (1/5) * 625  =    125 pounds

Here's the last one

It takes Tina  30miles / 45mph  =  2/3 of an hour to get to work  = 40 minutes

So......10 minutes earlier is 30 minutes.....so........to travel 30 miles in 30 minutes....she must travel at 1 mile per minute  =  60 mph   

(x^3-5x^2+7x-12)/(x-4) 

           x^2  -  x     +  3

x - 4 [ x^3  -5x^2  +  7x  -12  ] 

          x^3  -4x^2

         ___________________

                  -x^2   +  7x

                  -x^2  +   4x

                  ______________

                              3x   -  12

                              3x   -  12

                              ________

Because the degree is two, we either have two real roots or two complex roots

The roots are non-real because the discriminant is < 0

2x^2  + 4x +  7  = 0   subtract 7 from both sides

2x^2  +  4x  = -7

2 (x ^2 + 2x)  = -7    divide both sides by 2

x^2 + 2x   =  -7/2

Take 1/2 of 2  = 1.....square it  =  1   add it to both sides

 x^2 + 2x + 1  =  -7/2 + 1   factor the left, simplify the right

(x + 1) ^2  =  -5/2       take both roots

x + 1  =  ± √[ -5/2 ]    subtract 1  and simplify the right

x  = ± √[5/2] i    - 1