Multiply (3x+1) (x-6)

x = {-6, 0.3333333333}

Step-by-step explanation:

Simplifying

(3x + -1)(x + 6) = 0

Reorder the terms:

(-1 + 3x)(x + 6) = 0

Reorder the terms:

(-1 + 3x)(6 + x) = 0

Multiply (-1 + 3x) * (6 + x)

(-1(6 + x) + 3x * (6 + x)) = 0

((6 * -1 + x * -1) + 3x * (6 + x)) = 0

((-6 + -1x) + 3x * (6 + x)) = 0

(-6 + -1x + (6 * 3x + x * 3x)) = 0

(-6 + -1x + (18x + 3x2)) = 0

Combine like terms: -1x + 18x = 17x

(-6 + 17x + 3x2) = 0

Solving

-6 + 17x + 3x2 = 0

Solving for variable 'x'.

Factor a trinomial.

(-6 + -1x)(1 + -3x) = 0

Subproblem 1

Set the factor '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying

-6 + -1x = 0

Solving

-6 + -1x = 0

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

Add '6' to each side of the equation.

-6 + 6 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0

0 + -1x = 0 + 6

-1x = 0 + 6

Combine like terms: 0 + 6 = 6

-1x = 6

Divide each side by '-1'.

x = -6

Simplifying

x = -6

Subproblem 2

Set the factor '(1 + -3x)' equal to zero and attempt to solve:

Simplifying

1 + -3x = 0

Solving

1 + -3x = 0

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

Add '-1' to each side of the equation.

1 + -1 + -3x = 0 + -1

Combine like terms: 1 + -1 = 0

0 + -3x = 0 + -1

-3x = 0 + -1

Combine like terms: 0 + -1 = -1

-3x = -1

Divide each side by '-3'.

x = 0.3333333333

Simplifying

x = 0.3333333333

  b.   the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

so the change in y-value for function f is (6 )) = 9.

the table tells us

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).

no idea

step-by-step explanation: