Respuesta :

Answer:

h = 2

Step-by-step explanation:

6x  + 18  =  h (3x + 9)

To get the value of h, we simply need to make h subject of the formula;

To make h subject of the formula, we simply divide both-side of the equation by (3x + 9)

[tex]\frac{6x + 18}{3x + 9}[/tex]       =     [tex]\frac{h(3x + 9)}{(3x + 9)}[/tex]

(On the right hand side of the equation (3x+2) will cancel out (3x+2) leaving us with h)

[tex]\frac{6x + 18}{3x + 9}[/tex]       =      h

h  =   [tex]\frac{6x + 18}{3x + 9}[/tex]   ----------------(1)

We want to make the numerator and denominator look the same so that  we can cancel out, at the numerator, we can factor out 2 from 6x + 18

i.e 6x + 18 = 2 ( 3x + 9)

So we can  replace 6x + 18    by  2(3x + 9)  in equation (1)

h = [tex]\frac{2 (3x + 9)}{(3x +9)}[/tex]

( on the right hand side of the equation, (3x + 9) will cancel out (3x + 9) leaving us with just 2)

h = 2

We can plug in our h =2 in the initial equation

6x +  18   =  2(3x + 9)

6x + 18 = 6x + 18

This equation has an infinite number of solutions.

Therefore the value of constant h in the equation that can make the equation have an infinite number of solutions is 2

Answer:

For h=2 the equation will result in an infinite number of solutions.

Step-by-step explanation:

Given,

The expression is [tex]6x+18=h(3x+9)[/tex].

Need to find the value of h, so that the expression will have an infinite number of solutions.

Now, take the expression and solve it further.

[tex]6x+18=h(3x+9)\\6x+18=3hx+9h[/tex]

If the coefficient of the left-hand side and the coefficient of the right-hand side are equated, then the expression will result in an infinite number of solutions.

Thus,

[tex]3h=6\\h=2[/tex]

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https://brainly.com/question/8775925?referrer=searchResults