Solution
- 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:
[tex]-2\times x=-2x[/tex]- 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:
[tex]-2x-6[/tex]- 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:
[tex]-2x-6>-18[/tex]- Now that we have the inequality, we can proceed to solve for the unknown number x as follows;
[tex]\begin{gathered} -2x-6>-18 \\ \text{ Add 6 to both sides} \\ -2x>-18+6 \\ -2x>-12 \\ \text{ Divide both sides by -2} \\ \\ -\frac{2x}{-2}<-\frac{12}{-2} \\ \\ \therefore x<6 \\ \\ (\text{ Notice that the inequality sign changed because we divided both sides by a negative number\rparen} \end{gathered}[/tex]- Thus the solution is x < 6