Solve the inequalities

(i) −35<6x+7<1

Subtract -7 from all sides

-35 – 7 < 6x + 7 – 7 < 1 -7

-42 < 6x < -6

Dividing all sides by 6, we get

-7 < x < -1

(ii) $3x^{2} > 48$

Dividing both sides by 3, we get

$x^{2} > 16 \\ \\ \therefore x > \pm 4 \\ \\ x > 4\\ x < 4$