instructions: solve each inequality.\n1. $x - 14 > 6$\n2. $4 > x + 6$\n3. $x - 4 leq -5$\n4. $14 leq x…

Explanation:

Step1: Solve (x - 14>6)

Add 14 to both sides of the inequality: (x-14 + 14>6 + 14) (x>20)

Step2: Solve (4>x + 6)

Subtract 6 from both sides: (4-6>x+6 - 6) (-2>x) or (x < - 2)

Step3: Solve (x - 4\leq - 5)

Add 4 to both sides: (x-4 + 4\leq - 5+4) (x\leq - 1)

Step4: Solve (14\leq x - 3)

Add 3 to both sides: (14 + 3\leq x-3 + 3) (17\leq x) or (x\geq17)

Step5: Solve (15x\geq30)

Divide both sides by 15: (\frac{15x}{15}\geq\frac{30}{15}) (x\geq2)

Step6: Solve (x - 3<2)

Add 3 to both sides: (x-3 + 3<2 + 3) (x<5)

Step7: Solve (1\geq x - 11)

Add 11 to both sides: (1+11\geq x-11 + 11) (12\geq x) or (x\leq12)

Step8: Solve (\frac{x}{2}\geq3)

Multiply both sides by 2: (\frac{x}{2}\times2\geq3\times2) (x\geq6)

Answer:

1. (x>20)
2. (x < - 2)
3. (x\leq - 1)
4. (x\geq17)
5. (x\geq2)
6. (x<5)
7. (x\leq12)
8. (x\geq6)