How many solutions exist for the given equation? 1/2 (x 12) = 4x – 1 zero one two infinitely many

There's 1 solution.

Solve for  x by simplifying both sides of the equation, then isolating the variable.

x=2

Step-by-step explanation:

1/2(x+12)=4x−1

Step 1: Simplify both sides of the equation.

1/2(x+12)=4x−1

(1/2)(x)+(1/2)(12)=4x+−1(Distribute)

1/2x+6=4x+−1

1/2x+6=4x−1

Step 2: Subtract 4x from both sides.

1/2x+6−4x=4x−1−4x

−7/2x+6=−1

Step 3: Subtract 6 from both sides.

−7/2x+6−6=−1−6

−7/2x=−7

Step 4: Multiply both sides by 2/(-7).

(2/−7)*(−7/2x)=(2/−7)*(−7)

x=2

  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).