The expressions we have are:
[tex]\begin{gathered} 4x-7>5 \\ or \\ 5x+4\leq-6 \end{gathered}[/tex]
We need to solve each of these expressions, and since it is a compound inequality, the solution will be the solution of the first inequality OR the solution of the second inequality.
We start by solving:
[tex]4x-7>5[/tex]
The first step is to add 7 to both sides:
[tex]\begin{gathered} 4x-7+7>5+7 \\ 4x>12 \end{gathered}[/tex]
The next step is to divide both sides by 4:
[tex]\begin{gathered} \frac{4x}{4}>\frac{12}{4} \\ x>3 \end{gathered}[/tex]
We have the first part of the solution: x>3
Now we need to solve the second inequality:
[tex]5x+4\leq-6[/tex]
The first step is to subtract 4 to both sides:
[tex]\begin{gathered} 5x+4-4\leq-6-4 \\ 5x\leq-10 \end{gathered}[/tex]
And the second step is to divide both sides by 5:
[tex]\begin{gathered} \frac{5x}{5}\leq-\frac{10}{5} \\ x\leq-2 \end{gathered}[/tex]
We have the second part of the solution. And since the initial conditions are one inequality OR the other, the same goes to express the solution:
[tex]x\leq-2\text{ or x>}3[/tex]
ANSWER: OPTION D
[tex]x\leq-2\text{ or x>}3[/tex]
