Answer
a) $\lt$
b) $\leq$
c)$\leq$
d)$\gt$
Work Step by Step
In this exercise, we modify the initial equations to look like the second one:
a) $x\lt5; x-3\lt5-3; x-3\lt2$
b) $x\leq5; 3\times x \leq3\times5; 3x\leq 15 $ we note that the sign of the inequality doesn't change because we multiply by 3 $\gt$ 0
c) $x \geq2; -3 \times x \leq 2\times -3 ; -3x \leq-6 $ the sign of the inequality changes because we are multiplying by a negative number
d) $x\lt-2 ; -1 \times x \gt -1 \times -2 ; -x\gt 2 $ the sign of the inequality changes because we are multiplying by a negative number
