Question 1.34: Solve the following inequalities: (a) 3t+1 > t+7        ......

(a) 3 t+1>t+7

2 t+1>7 subtracting t from both sides

2 t>6 subtracting 1 from both sides

t>3 dividing both sides by 2

Hence all values of t greater than 3 satisfy the inequality.

(b) 2-3 z \leqslant 6+z

-3 z \leqslant 4+z  subtracting 2 from both sides

-4 z \leqslant 4  subtracting z from both sides

z \geqslant-1  dividing both sides by —4, remembering to reverse the inequality

Hence all values of z greater than or equal to —1 satisfy the inequality.