Question

① n + 12 - 4 = - 8
② 4x = 36
③ v/3 = - 11
④ w - 9 = 22
⑤ - 7t = 42
⑥ - 1/5y = - 20
⑦ - 32 = x + (- 20)
⑧ - 48 = 2q
⑨ 13 = n/10
⑩ - 50 = 19 + p
⑪ - 15r = - 75
⑫ 14 = - u/4
⑬ x - (- 16) = 44
⑭ 42 = 6d
⑮ 1/8y = - 12
⑯ - 4 = 11 + m
⑰ - x = 35
⑱ - 3 = - a/13
⑲ - 18 + z = 18
⑳ - 125 = - 5k

Explanation:

Step1: Solve \(n + 12-4=-8\)

Subtract 12 and add 4 on both sides: \(n=-8 - 12+4=-16\)

Step2: Solve \(4x = 36\)

Divide both sides by 4: \(x=\frac{36}{4}=9\)

Step3: Solve \(\frac{v}{3}=-11\)

Multiply both sides by 3: \(v=-11\times3=-33\)

Step4: Solve \(w - 9 = 22\)

Add 9 to both sides: \(w=22 + 9=31\)

Step5: Solve \(-7t = 42\)

Divide both sides by - 7: \(t=\frac{42}{-7}=-6\)

Step6: Solve \(-\frac{1}{5}y=-20\)

Multiply both sides by - 5: \(y=-20\times(-5)=100\)

Step7: Solve \(-32=x+(-20)\)

Add 20 to both sides: \(x=-32 + 20=-12\)

Step8: Solve \(-48 = 2q\)

Divide both sides by 2: \(q=\frac{-48}{2}=-24\)

Step9: Solve \(13=\frac{n}{10}\)

Multiply both sides by 10: \(n=13\times10 = 130\)

Step10: Solve \(-50=19 + p\)

Subtract 19 from both sides: \(p=-50 - 19=-69\)

Step11: Solve \(-15r=-75\)

Divide both sides by - 15: \(r=\frac{-75}{-15}=5\)

Step12: Solve \(14=\frac{-u}{4}\)

Multiply both sides by - 4: \(u=14\times(-4)=-56\)

Step13: Solve \(x-(-16)=44\)

Simplify to \(x + 16=44\), then subtract 16 from both sides: \(x=44-16 = 28\)

Step14: Solve \(42 = 6d\)

Divide both sides by 6: \(d=\frac{42}{6}=7\)

Step15: Solve \(\frac{1}{8}y=-12\)

Multiply both sides by 8: \(y=-12\times8=-96\)

Step16: Solve \(-4=11 + m\)

Subtract 11 from both sides: \(m=-4-11=-15\)

Step17: Solve \(-x = 35\)

Multiply both sides by - 1: \(x=-35\)

Step18: Solve \(-3=\frac{-a}{13}\)

Multiply both sides by - 13: \(a=-3\times(-13)=39\)

Step19: Solve \(-18+z = 18\)

Add 18 to both sides: \(z=18 + 18=36\)

Step20: Solve \(-125=-5k\)

Divide both sides by - 5: \(k=\frac{-125}{-5}=25\)

Answer:

The solutions for the variables are: \(n=-16,130\); \(x = 9,28,-35\); \(v=-33\); \(w=31\); \(t=-6\); \(y = 100,-96\); \(q=-24\); \(p=-69\); \(r = 5\); \(u=-56\); \(d=7\); \(m=-15\); \(a=39\); \(z=36\); \(k=25\)