Question

Which values are part of the solution set based on the result of the inequality

Answer 1

The possible solutions are;

`0,\text{ -3, 3.4, -3.2}`

Step-by-step explanation:

Given the inequality;

`-3(2x+7)\leq(1)/(2)x`

Let us solve for x;

`\begin{gathered} -3(2x+7)\leq(1)/(2)x \\ \text{expanding;} \\ -6x-21\leq(1)/(2)x \\ \text{ multiply through by 2;} \\ 2(-6x)-21(2)\leq2((1)/(2)x) \\ -12x-42\leq x \\ \text{collecting the like terms;} \\ -12x-x\leq42 \\ -13x\leq42 \\ \text{divide both sides by -13;} \\ x\ge(42)/(-13) \\ x\ge-3(3)/(13) \end{gathered}`

Therefore, the solution to the inequality is;

`\begin{gathered} x\ge-3(3)/(13) \\ or \\ x\ge-3.23 \end{gathered}`

So, from the options, the possible solutions are;

`0,\text{ -3, 3.4, -3.2}`