Question

-\frac{1}{3}x=-15 \\\\ \frac{3}{4}y = 6 \\\\ -\frac{2}{3}v = 14 \\\\ -\frac{9}{8}y=-27 \\\\ -8k = 248 \\\\ \frac{3}{10}m = 15 \\\\ -11t=-132 \\\\ -\frac{5}{3}x = 20

Explanation:

Step1: Solve for x in \(-\frac{1}{3}x=-15\)

Multiply both sides by -3: \(x = (-15)\times(-3)=45\)

Step2: Solve for y in \(\frac{3}{4}y = 6\)

Multiply both sides by \(\frac{4}{3}\): \(y=6\times\frac{4}{3}=8\)

Step3: Solve for v in \(-\frac{2}{3}v = 14\)

Multiply both sides by \(-\frac{3}{2}\): \(v=14\times(-\frac{3}{2})=-21\)

Step4: Solve for y in \(-\frac{9}{8}y=-27\)

Multiply both sides by \(-\frac{8}{9}\): \(y=(-27)\times(-\frac{8}{9}) = 24\)

Step5: Solve for k in \(-8k = 248\)

Divide both sides by -8: \(k=\frac{248}{-8}=-31\)

Step6: Solve for m in \(\frac{3}{10}m = 15\)

Multiply both sides by \(\frac{10}{3}\): \(m=15\times\frac{10}{3}=50\)

Step7: Solve for t in \(-11t=-132\)

Divide both sides by -11: \(t=\frac{-132}{-11}=12\)

Step8: Solve for x in \(-\frac{5}{3}x = 20\)

Multiply both sides by \(-\frac{3}{5}\): \(x=20\times(-\frac{3}{5})=-12\)

Answer:

1. \(x = 45\)
2. \(y = 8\)
3. \(v=-21\)
4. \(y = 24\)
5. \(k=-31\)
6. \(m = 50\)
7. \(t = 12\)
8. \(x=-12\)