Question

1. -18 < n + (-3)
2. -15 + 6 ≥ -14
3. 4 ≤ v - 5
4. x - (-7) > 4
5. 9 < -1 + \frac{n}{12}
6. -10 ≤ \frac{a}{8} - 9
7. -3 > -4 + \frac{k}{9}
8. -7 ≥ \frac{-4 + p}{2}
9. \frac{7 + x}{-2} ≥ 2
10. 3 + 7m ≤ -18
11. -4m - 1 < -37
12. 2(-7 + x) > -2
13. -69 ≤ -1 - 4r
14. 2(4 + n) > -22

Explanation:

17) Step1: Simplify right-hand side

$ -18 \leq a - 3 $

17) Step2: Isolate $a$ (add 3)

$ a \geq -18 + 3 = -15 $

18) Step1: Isolate $b$ (add 15)

$ b \geq -34 + 15 = -19 $

19) Step1: Isolate $v$ (add 5)

$ v \geq 4 + 5 = 9 $

20) Step1: Simplify left-hand side

$ x + 7 > 4 $

20) Step2: Isolate $x$ (subtract 7)

$ x > 4 - 7 = -3 $

21) Step1: Isolate fraction (add 1)

$ 1 < \frac{a}{12} $

21) Step2: Isolate $a$ (multiply by 12)

$ a > 1 \times 12 = 12 $

22) Step1: Isolate fraction (add 9)

$ -10 + 9 \leq \frac{a}{8} \implies -1 \leq \frac{a}{8} $

22) Step2: Isolate $a$ (multiply by 8)

$ a \geq -1 \times 8 = -8 $

23) Step1: Isolate fraction (add 4)

$ -3 + 4 > \frac{h}{9} \implies 1 > \frac{h}{9} $

23) Step2: Isolate $h$ (multiply by 9)

$ h < 1 \times 9 = 9 $

24) Step1: Isolate numerator (multiply by 2)

$ -7 \times 2 \geq -4 + p \implies -14 \geq -4 + p $

24) Step2: Isolate $p$ (add 4)

$ p \leq -14 + 4 = -10 $

25) Step1: Eliminate denominator (multiply by -2, reverse inequality)

$ 7 + x \leq 2 \times (-2) = -4 $

25) Step2: Isolate $x$ (subtract 7)

$ x \leq -4 - 7 = -11 $

26) Step1: Isolate term with $m$ (subtract 3)

$ 7m \leq -18 - 3 = -21 $

26) Step2: Isolate $m$ (divide by 7)

$ m \leq \frac{-21}{7} = -3 $

27) Step1: Isolate term with $m$ (add 1)

$ -4m < -37 + 1 = -36 $

27) Step2: Isolate $m$ (divide by -4, reverse inequality)

$ m > \frac{-36}{-4} = 9 $

28) Step1: Divide both sides by 2

$ -7 + x > \frac{-2}{2} = -1 $

28) Step2: Isolate $x$ (add 7)

$ x > -1 + 7 = 6 $

29) Step1: Isolate term with $r$ (add 1)

$ -69 + 1 \leq -4r \implies -68 \leq -4r $

29) Step2: Isolate $r$ (divide by -4, reverse inequality)

$ r \geq \frac{-68}{-4} = 17 $

30) Step1: Divide both sides by 2

$ 4 + n > \frac{-22}{2} = -11 $

30) Step2: Isolate $n$ (subtract 4)

$ n > -11 - 4 = -15 $

Answer:

1. $a \geq -15$ (graph: closed dot at -15, arrow right)
2. $b \geq -19$ (graph: closed dot at -19, arrow right)
3. $v \geq 9$ (graph: closed dot at 9, arrow right)
4. $x > -3$ (graph: open dot at -3, arrow right)
5. $a > 12$ (graph: open dot at 12, arrow right)
6. $a \geq -8$ (graph: closed dot at -8, arrow right)
7. $h < 9$ (graph: open dot at 9, arrow left)
8. $p \leq -10$ (graph: closed dot at -10, arrow left)
9. $x \leq -11$ (graph: closed dot at -11, arrow left)
10. $m \leq -3$ (graph: closed dot at -3, arrow left)
11. $m > 9$ (graph: open dot at 9, arrow right)
12. $x > 6$ (graph: open dot at 6, arrow right)
13. $r \geq 17$ (graph: closed dot at 17, arrow right)
14. $n > -15$ (graph: open dot at -15, arrow right)