Question

6x+18=h(3x+9) what value the constant h in the equation shown below will result in a infinite number of solutions

Answer 1

For there to be an infinite number of solutions, the quantity on the left side of the equation must be the same as on the right.
First, distribute the equation to get 
6x + 18 = 3xh + 9h
If h = 2, the equation on the right would also be 6x + 18 which would yield the same equation and hence an infinite number of solutions
So the answer is h = 2

Answer 2

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)

$\frac{6x + 18}{3x + 9}$       =     $\frac{h(3x + 9)}{(3x + 9)}$

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

$\frac{6x + 18}{3x + 9}$       =      h

h  =   $\frac{6x + 18}{3x + 9}$   ----------------(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 = $\frac{2 (3x + 9)}{(3x +9)}$

( 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