We are asked to simplify the following inequalities: (a) $2x + 3 < 7$ (b) $5t + 6 > 21$ (c) $3x - 5 \ge 16$ (d) $1.5z + 1 \le 2$

1. Problem Description

We are asked to simplify the following inequalities:

(a) $2x + 3 < 7$

(b) $5t + 6 > 21$

(c) $3x - 5 \ge 16$

(d) $1.5z + 1 \le 2$

2. Solution Steps

(a) $2x + 3 < 7$

Subtract 3 from both sides:

$2x + 3 - 3 < 7 - 3$

$2x < 4$

Divide both sides by 2:

$\frac{2x}{2} < \frac{4}{2}$

$x < 2$

(b) $5t + 6 > 21$

Subtract 6 from both sides:

$5t + 6 - 6 > 21 - 6$

$5t > 15$

Divide both sides by 5:

$\frac{5t}{5} > \frac{15}{5}$

$t > 3$

(c) $3x - 5 \ge 16$

Add 5 to both sides:

$3x - 5 + 5 \ge 16 + 5$

$3x \ge 21$

Divide both sides by 3:

$\frac{3x}{3} \ge \frac{21}{3}$

$x \ge 7$

(d) $1.5z + 1 \le 2$

Subtract 1 from both sides:

$1.5z + 1 - 1 \le 2 - 1$

$1.5z \le 1$

Divide both sides by 1.5:

$\frac{1.5z}{1.5} \le \frac{1}{1.5}$

$z \le \frac{1}{\frac{3}{2}}$

$z \le \frac{2}{3}$

3. Final Answer

(a) $x < 2$

(b) $t > 3$

(c) $x \ge 7$

(d) $z \le \frac{2}{3}$