If f(x) is a linear function and the domain of f(x) is the set of all real numbers, which statement cannot be true?

the graph of f(x) has zero x-intercepts.
the graph of f(x) has exactly one x-intercept.
the graph of f(x) has exactly two x-intercepts.
the graph of f(x) has infinitely many x-intercepts.

C. The graph of f(x) has exactly two x-intercepts.

Step-by-step explanation:

We have been told that f(x) is a linear function and the domain of f(x) is the set of all real numbers. We are asked to find the statement, which is not true for our given function.

Let us check our given choices one by one.

A. The graph of f(x) has zero x-intercepts.

We know that graph of a linear function is a straight line. For a horizontal line the graph of f(x) has zero x-intercepts for all the horizontal lines except that is the equation of x-axis.

Therefore, statement A is true.

B. The graph of f(x) has exactly one x-intercept.

We know that a linear function crosses exactly at one place, therefore, statement B is true as well.

C. The graph of f(x) has exactly two x-intercepts.

We know that a linear function can have at-most one x-intercept, therefore, statement C is not true.

D. The graph of f(x) has infinitely many x-intercepts.

When the linear function coincides with x-axis that is , then each point on the line is x-intercept.

Therefore, statement D is true as well.

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step-by-step explanation:

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .