Option C: [tex](-\infty, \infty)[/tex] is the solution in interval notation.
Explanation:
The expression is [tex]-7 x>-35 \text { or } x+7>4[/tex]
First let us solve the expression [tex]-7 x>-35[/tex]
Dividing both sides by -7, we have,
[tex]x<5[/tex] ------------(1)
Similarly solving the expression [tex]x+7>4[/tex]
Subtracting both sides by 7, we get,
[tex]x>-3[/tex] --------------(2)
Substituting (1) and (2) in the original equation [tex]-7 x>-35 \text { or } x+7>4[/tex], we get,
[tex]x<5 or x>-3[/tex]
Thus, writing it in interval notation, we have,
[tex](-\infty,5) U (-3,\infty)[/tex]
Thus, the union of the two intervals in [tex](-\infty, \infty)[/tex]
Hence, Option C is the correct answer.
