Question

1
7 ≥ 3x - 1
7 > -x + 3

2
y < 3
y > -2x - 1

3
y < -\frac{1}{3}x + 2
y > -\frac{5}{3}x - 2

Explanation:

1. Solve first system of inequalities

Step1: Isolate $3x$ in first inequality

$7 + 1 \geq 3x$
$8 \geq 3x$

Step2: Solve for $x$

$x \leq \frac{8}{3}$

Step3: Isolate $x$ in second inequality

$7 - 3 > -x$
$4 > -x$

Step4: Solve for $x$

$x > -4$

Step5: Combine solutions

$-4 < x \leq \frac{8}{3}$

2. Solve second system of inequalities

Step1: Identify given bounds

$y < 3$ and $y > -2x - 1$

Step2: Combine into compound inequality

$-2x - 1 < y < 3$

3. Solve third system of inequalities

Step1: Identify given bounds

$y < -\frac{1}{3}x + 2$ and $y > -\frac{5}{3}x - 2$

Step2: Combine into compound inequality

$-\frac{5}{3}x - 2 < y < -\frac{1}{3}x + 2$

Answer:

1. $-4 < x \leq \frac{8}{3}$
2. $-2x - 1 < y < 3$
3. $-\frac{5}{3}x - 2 < y < -\frac{1}{3}x + 2$