f(x)=23x-12

Create a list of the coefficients of the function except the leading coefficient of 1.

23,1,-12

Arrange the terms in ascending order.

b1=|23|,|1|,|-12|

The maximum value is the largest value in the arranged data set.

b1=|-12|

The absolute value is the distance between a number and zero. The distance between -12 and 0 is 12.

b1=12+1

Add 12 and 1.

b1=13

b1=13

Simplify each term.

23 is approximately 0.6‾ which is positive so remove the absolute value

b2=23+|1|+|-12|

The absolute value is the distance between a number and zero. The distance between 0 and 1 is 1.

b2=23+1+|-12|

The absolute value is the distance between a number and zero. The distance between -12 and 0 is 12.

b2=23+1+12

b2=23+1+12

Find the common denominator.

Write 1 as a fraction with denominator 1.

b2=23+11+12

Multiply 11 by 33.

b2=23+11⋅33+12

Multiply 11 and 33.

b2=23+33+12

Write 12 as a fraction with denominator 1.

b2=23+33+121

Multiply 121 by 33.

b2=23+33+121⋅33

Multiply 121 and 33.

b2=23+33+12⋅33

b2=23+33+12⋅33

Combine fractions.

Combine fractions with similar denominators.

b2=2+3+12⋅33

Multiply 12 by 3.

b2=2+3+363

b2=2+3+363

Simplify the numerator.

Add 2 and 3.

b2=5+363

Add 5 and 36.

b2=413

b2=413

Arrange the terms in ascending order.

b2=1,413

The maximum value is the largest value in the arranged data set.

b2=413

b2=413

Take the smaller bound option between b1=13 and b2=413.

Smaller Bound: 13

Every real root on f(x)=23x-12 lies between -13 and 13.

-13 and 13

Find the Bounds of the Zeros f(x)=2/3x-12