Question

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

Answer 1

Answer:

The possible solutions are;

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

Explanation:

Given the inequality;

$-3(2x+7)\leq\frac{1}{2}x$

Let us solve for x;

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

Therefore, the solution to the inequality is;

$\begin{gathered} x\ge-3\frac{3}{13} \\ or \\ x\ge-3.23 \end{gathered}$

So, from the options, the possible solutions are;

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