HELP PLZ
Solve each proportion for the variable

x = -1

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    4/12-((x+2)/(2*x+5))=0

                    x + 2

Simplify   ——————

                    2x + 5        

                           1

Simplify again   —

                           3

1       (x + 2)

— - —————  = 0  

3       2x + 5

Find the Least Common Multiple

     The left denominator is :       3  

     The right denominator is :       2x+5  

       Number of times each prime factor

       appears in the factorization of:

Prime  

Factor   Left  

Denominator   Right  

Denominator   L.C.M = Max

{Left , Right}  

3101

Product of all  

Prime Factors  313

                 Number of times each Algebraic Factor

           appears in the factorization of:

   Algebraic    

   Factor      Left  

Denominator   Right  

Denominator   L.C.M = Max  

{Left , Right}  

2x+5  011

     Least Common Multiple:

     3 • (2x+5)  

Denote the Least Common Multiple by  L.C.M  

Denote the Left Multiplier by  Left_M  

Denote the Right Multiplier by  Right_M  

Denote the Left Deniminator by  L_Deno  

Denote the Right Multiplier by  R_Deno  

Left_M = L.C.M / L_Deno = 2x+5

Right_M = L.C.M / R_Deno = 3

Two fractions are called equivalent if they have the same numeric value.

For example :  1/2   and  2/4  are equivalent,  y/(y+1)2   and  (y2+y)/(y+1)3  are equivalent as well.

To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.

  L. Mult. • L. Num.                     2x+5    

  ——————————  =   ——————————

        L.C.M                               3 • (2x+5)

  R. Mult. • R. Num.                (x+2) • 3

  ——————————  =   ——————————

        L.C.M                            3 • (2x+5)

Add the two equivalent fractions which now have a common denominator . Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

2x + 5 - ((x + 2) • 3)                  -x - 1    

———————————  =  —————————

       3 • (2x + 5)                     3 • (2x + 5)

Pull out like factors :

  -x - 1  =   -1 • (x + 1)  

            -x - 1    

 —————————— = 0  

         3 • (2x + 5)

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now, to get rid of the denominator, multiply both sides of the equation by the denominator.

        -x - 1  

 ——————— • 3 • (2x + 5) = 0 • 3 • (2x + 5)

   3 • (2x + 5)

Now, on the left hand side, the  3 • 2x + 5  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

  -x - 1  = 0

Solving a Single Variable Equation:

Solve  :    -x - 1 = 0  

Add  1  to both sides of the equation :  

                     -x = 1

Multiply both sides of the equation by (-1) :  x = -1

g(x) = x² + 2

step-by-step explanation:

it is given that the graphs are the same shape.

the only difference is that the red graph is 2 units higher than the blue graph.

that is to say that the red graph is simply the blue graph that has been moved vertically by 2 units in the positive y direction.

hence

g(x) = f(x) + 2

or

g(x) = x² + 2

true

step-by-step explanation:

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