Question

solve the equation. check your solution.

1. $2v + 7 = 3$
2. $4b + 3 = -9$
3. $17 = 5k - 2$
4. $-6t - 7 = 17$
5. $8n + 16.2 = 1.6$
6. $-5g + 2.3 = -18.8$
7. $2t - 5 = -10$
8. $-4p + 9 = -5$
9. $11 = -5x - 2$
10. $4 + 2.2h = -3.7$
11. $-4.8f + 6.4 = -8.48$
12. $7.3y - 5.18 = -51.9$

Explanation:

Step1: Solve equation 6: \(2v + 7 = 3\)

Subtract 7 from both sides: \(2v = 3 - 7 = -4\)
Divide by 2: \(v = \frac{-4}{2} = -2\)
Check: \(2(-2) + 7 = -4 + 7 = 3\), correct.

Step2: Solve equation 7: \(4b + 3 = -9\)

Subtract 3: \(4b = -9 - 3 = -12\)
Divide by 4: \(b = \frac{-12}{4} = -3\)
Check: \(4(-3) + 3 = -12 + 3 = -9\), correct.

Step3: Solve equation 8: \(17 = 5k - 2\)

Add 2: \(5k = 17 + 2 = 19\)
Divide by 5: \(k = \frac{19}{5} = 3.8\)
Check: \(5(3.8) - 2 = 19 - 2 = 17\), correct.

Step4: Solve equation 9: \(-6t - 7 = 17\)

Add 7: \(-6t = 17 + 7 = 24\)
Divide by -6: \(t = \frac{24}{-6} = -4\)
Check: \(-6(-4) - 7 = 24 - 7 = 17\), correct.

Step5: Solve equation 10: \(8n + 16.2 = 1.6\)

Subtract 16.2: \(8n = 1.6 - 16.2 = -14.6\)
Divide by 8: \(n = \frac{-14.6}{8} = -1.825\)
Check: \(8(-1.825) + 16.2 = -14.6 + 16.2 = 1.6\), correct.

Step6: Solve equation 11: \(-5g + 2.3 = -18.8\)

Subtract 2.3: \(-5g = -18.8 - 2.3 = -21.1\)
Divide by -5: \(g = \frac{-21.1}{-5} = 4.22\)
Check: \(-5(4.22) + 2.3 = -21.1 + 2.3 = -18.8\), correct.

Step7: Solve equation 12: \(2t - 5 = -10\)

Add 5: \(2t = -10 + 5 = -5\)
Divide by 2: \(t = \frac{-5}{2} = -2.5\)
Check: \(2(-2.5) - 5 = -5 - 5 = -10\), correct.

Step8: Solve equation 13: \(-4p + 9 = -5\)

Subtract 9: \(-4p = -5 - 9 = -14\)
Divide by -4: \(p = \frac{-14}{-4} = 3.5\)
Check: \(-4(3.5) + 9 = -14 + 9 = -5\), correct.

Step9: Solve equation 14: \(11 = -5x - 2\)

Add 2: \(-5x = 11 + 2 = 13\)
Divide by -5: \(x = \frac{13}{-5} = -2.6\)
Check: \(-5(-2.6) - 2 = 13 - 2 = 11\), correct.

Step10: Solve equation 15: \(4 + 2.2h = -3.7\)

Subtract 4: \(2.2h = -3.7 - 4 = -7.7\)
Divide by 2.2: \(h = \frac{-7.7}{2.2} = -3.5\)
Check: \(4 + 2.2(-3.5) = 4 - 7.7 = -3.7\), correct.

Step11: Solve equation 16: \(-4.8f + 6.4 = -8.48\)

Subtract 6.4: \(-4.8f = -8.48 - 6.4 = -14.88\)
Divide by -4.8: \(f = \frac{-14.88}{-4.8} = 3.1\)
Check: \(-4.8(3.1) + 6.4 = -14.88 + 6.4 = -8.48\), correct.

Step12: Solve equation 17: \(7.3y - 5.18 = -51.9\)

Add 5.18: \(7.3y = -51.9 + 5.18 = -46.72\)
Divide by 7.3: \(y = \frac{-46.72}{7.3} = -6.4\)
Check: \(7.3(-6.4) - 5.18 = -46.72 - 5.18 = -51.9\), correct.

Answer:

1. \(v = -2\)
2. \(b = -3\)
3. \(k = 3.8\)
4. \(t = -4\)
5. \(n = -1.825\)
6. \(g = 4.22\)
7. \(t = -2.5\)
8. \(p = 3.5\)
9. \(x = -2.6\)
10. \(h = -3.5\)
11. \(f = 3.1\)
12. \(y = -6.4\)