Question

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

Answer 1

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

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