Explanation:
Part A:
The question is given below as
[tex]\begin{gathered} whenx=0,evaluate \\ -\frac{3}{4}x-4= \end{gathered}[/tex]By putting x=0, we will have that
[tex]\begin{gathered} \begin{equation*} -\frac{3}{4}x-4 \end{equation*} \\ -\frac{3}{4}(0)-4 \\ =-4 \end{gathered}[/tex]Hence,
The final answer for part A is
[tex]\Rightarrow-4[/tex]Part B:
[tex]\begin{gathered} solve, \\ -\frac{3}{4}x-4=-6 \end{gathered}[/tex]add 4 to both sides
[tex]\begin{gathered} -\frac{3}{4}x-4=-6 \\ -\frac{3}{4}x-4+4=-6+4 \\ -\frac{3}{4}x=-2 \\ coess\text{ multiply, we will have} \\ -3x=-2\times4 \\ -3x=-8 \\ divide\text{ both sides by -3} \\ \frac{-3x}{-3}=-\frac{8}{-3} \\ x=\frac{8}{3} \end{gathered}[/tex]Hence,
The final answer for part B is
[tex]\Rightarrow x=\frac{8}{3}[/tex]Part C:
[tex]-\frac{3}{4}x-4>-6[/tex]Add 4 to both sides, we will have
[tex]\begin{gathered} -\frac{3}{4}x-4\gt-6 \\ -\frac{3}{4}x-4+4\gt-6+4 \\ -\frac{3}{4}x>-2 \\ cross\text{ multiply} \\ -3x>-2\times4 \\ -3x>-8 \\ divide\text{ bth sides by -3} \\ \frac{-3x}{-3}>-\frac{8}{-3}(the\text{ sighn will be reversed\rparen} \\ x<\frac{8}{3}(0\text{ is a solution\rparen} \end{gathered}[/tex]Hence,
The final answer for part C is YES
Part D:
[tex]\begin{gathered} -\frac{3}{4}x-4\gt-6 \\ -\frac{3}{4}x-4+4\gt-6+4 \\ -\frac{3}{4}x>-2 \\ cross\text{ multiply} \\ -3x>-2\times4 \\ -3x>-8 \\ divide\text{ bth sides by -3} \\ \frac{-3x}{-3}>-\frac{8}{-3}(the\text{ sighn will be reversed\rparen} \\ x<\frac{8}{3} \\ hence,in\text{ interval notation we will have the final answer be} \\ (-\infty,\frac{8}{3}) \end{gathered}[/tex]Hence,
The final answer for part D is given below as
[tex]\Rightarrow(-\infty,\frac{8}{3})[/tex]