Question

5) Write and solve an inequality for the following:Six less than the product of -2 and a number is greater than -18.

Answer 1

- Let the unknown number be x. It is this number we are trying to solve for.

- We are told that "Six less than the product of -2 and a number...".

- The product of -2 and a number can be written as:

`-2* x=-2x`

- The same statement says that we need to make the product of -2 and a number less by 6. That is, we subtract 6 from the product of -2 and a number.

- Thus, we can say:

`-2x-6`

- The above mathematical statement implies "Six less than the product of -2 and a number...".

- Next, we are told that everything is greater than -18. Thus, we can conclude the inequality as follows:

`-2x-6>-18`

- Now that we have the inequality, we can proceed to solve for the unknown number x as follows;

`\begin{gathered} -2x-6>-18 \\ \text{ Add 6 to both sides} \\ -2x>-18+6 \\ -2x>-12 \\ \text{ Divide both sides by -2} \\ \\ -(2x)/(-2)<-(12)/(-2) \\ \\ \therefore x<6 \\ \\ (\text{ Notice that the inequality sign changed because we divided both sides by a negative number\rparen} \end{gathered}`

- Thus the solution is x < 6