Solve the following inequality

|-2x+1|<13

1+4x

2

−4x>13+3x

2

Step-by-step explanation:

x

2

−4x−12>0

(x−6)(x+2)>0

xϵ(−∞,−2)∪(6,∞)

-6 < x < 7

Step-by-step explanation:

-2x + 1 ≥ 0

-2x ≥ -1

x ≤ 1/2

if x ≤ 1/2

-2x + 1 < 13

-2x < 12

x > -6

-6 < x ≤ 1/2

if x > 1/2

2x-1 < 13

2x < 14

x < 7

1/2 < x < 7

-6 < x < 7

Part a) The graph in the attached figure

Part b) The units rate of change is 9

Step-by-step explanation:

we know that

A relationship between two variables, t, and d, represent a proportional variation if it can be expressed in the form  or

step 1

Find the constant of proportionality k

For

substitute

the linear equation is equal to

using a graphing tool

see the attached figure

step 2

Find the unit rate

we know that

In a proportional relationship the constant of proportionality k is equal to the unit rate of change or slope m of the line, because the line passes through the origin

so

The units rate of change is 9

That means> A change of 1 unit in t correspond to a change of 9 units in d

see the attached figure to better understand the problem