Please show all the work needed to solve the problem! Evaluate the expression for the given value of the variable.

| − 4 b − 8 | + ∣ ∣ − 1 − b 2 ∣ ∣ + 2 b 3 -4b-8+-1-b2+2b3 ; b = − 2 b=-2

The value of the variable is -21,21 and 11 for solving the modulus  for different expressions.

Step-by-step explanation:

The given expression is in modulus which means that the values of the expression can be both negative and positive . So we are removing modulus but evaluating both values.

− 4 b − 8   − 1 − b 2  + 2 b 3

We did not change any sign taking the positive values into account.

So adding and subtracting would give

− 4 b − 9 − b 2  + 2 b 3

Now putting the value of b= -2

− 4 (-2) − 9 −  (-2)^ 2  + 2  (-2) ^3

= 8-9-4-16= -21

Now again solving for taking  value of last expression of the mod to be negative

| − 4 b − 8 | + ∣ ∣ − 1 − b 2 ∣ ∣ + 2 b 3 ∣

− 4 b − 8   − 1 − b 2  -2 b 3

− 4 (-2) − 9 −  (-2)^ 2  - 2  (-2) ^3

= 8-9-4+16= 11

Now  solving for taking  value of last two  expressions of the mod to be negative

| − 4 b − 8 | + ∣ ∣ − 1 − b 2 ∣ ∣ + 2 b 3 ∣

− 4 b − 8   +1 +b 2  -2 b 3

− 4 (-2) − 7 + (-2)^ 2  - 2  (-2) ^3

= 8-7 + 4+16= 21

And  solving for taking  value of all  expressions of the mod to be negative

| − 4 b − 8 | + ∣ ∣ − 1 − b 2 ∣ ∣ + 2 b 3 ∣

+ 4 b + 8   +1 +b 2  -2 b 3

+4 (-2) + 9 + (-2)^ 2  - 2  (-2) ^3

= -8 +9 + 4+16= 21

Solving for taking the value of first and last expressions of the mod to be negative

| − 4 b − 8 | + ∣ ∣ − 1 − b 2 ∣ ∣ + 2 b 3 ∣

+ 4 b + 8   -1 -b 2  -2 b 3

+4 (-2) + 7 - (-2)^ 2  - 2  (-2) ^3

= -8 +7 - 4+16= 11

So we are getting the values of -21 and 21 and 11

system of linear equation

step-by-step explanation:

as given in the data

a= 20 , b= -12

let us suppose that it is a straight line equation

now we know the formula for the system of linear equation

b= ma + c )

here m is slope of a straight line which is equal to formula

m=   (ii)

and here c is a constant

now putting the value of a and b in equation (ii)

m=

m=

putting the value of a,b and m in equation (i) gives us

-12 = + c

-12=-12 + c

adding 12 to both sides

-12 +12 = -12 +12 +c

0 =c

or c=0

as the value of the constant is zero which gives us that it is a linear equation and this order pair satisfies the system of linear equations.