Chapter ISG, Problem 1.2.10P

To determine

Determine whether each statement about the expression $a^2-5\left(b+2\right)$ is always,sometimes or never true.

Answer to Problem 1.2.10P

Always True

  $90-5b<100$

Explanation of Solution

Given information:

  $a^2-5\left(b+2\right)$

If a= 10 then the value of the expression is less then 100

  $a^2-5\left(b+2\right)$

Put the value a =10 in the given equation and expression is less then 100

  ${10}^2-5\left(b+2\right)<100$

Solve the power of 10

  $100-5\left(b+2\right)<100$

Multiply -5 in the bracket term

  $100-5b-10<100$

Hence, on subtracting, the final answer is-

  $90-5b<100$

If there is any value of b in the equation.For example

Put the b = 5 in the above equation

Let b = 5

  $90-5\times 5<100$

Multiply by 5 to 5

  $90-25<100$

By subtracting the answer is

  $65<100$

It will be always true on the any value of b