Question

Five times the sum of a number and 27 is greater than or equal to six times the sum of that number and 26. What is thesolution set of this problem?O (-0, -21)O (-00,-21]o [-21, 700)O (21, +00)

Answer 1

This is a question of inequalities.

We need to develop a mathematical model for the inequality.

Let x represent the unknown number:

`\begin{gathered} 5(x+27)\ge6(x+26) \\ \text{Expanding:} \\ 5x+135\ge6x+156 \\ \text{Subtracting 135 from both sides give:} \\ 5x\ge6x+21 \\ \text{Subtracting 6x from both sides give:} \\ -x\ge21 \\ \text{Dividing both sides by -1 gives:} \\ x\leq-21 \end{gathered}`

The solution set goes from minus infinity to -21 mathematically expressed as:

`(-\infty,-21)`

OPTION B