How many solutions does 3(4x−8)=−24+12x have?

All real numbers

Step-by-step explanation:

Question: 3(4x-8)=24+12x

Step 1: Get rid of parenthesis.

12x-24=24+12

Step 2: Rearrange so like terms are together

12x-12x=24-24

Step 3: solve for x

0=0

So, there are an infinite number of solutions.

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let f (x ) is a function and c be a positive real number,   the graph of the function g (x ) = f (cx ) is represented as follows.

when, c > 1,   the function compresses it in the x - direction.

when, 0 < c < 1, the function stretches it.

the function is g ( x ) = (9x )2.

the heighest power of x in g ( x ) = (9x )2 is 2, so the parent function is square function.

the equation of parent function is f ( x ) = x 2 .

the function is g ( x ) = (9x )2 and the parent function is f ( x ) = x 2 .

so, the functions f and g have the following relationship.

g ( x ) = f ( 9x ).

compare the function g ( x ) = f ( 9x ) with g (x ) = f (cx ).

c = 9 ( > 1 ).

so, the function g (x ) = (9x )2 compresses it in the x - direction.

step-by-step explanation: