Question

1. -3x + 5.4 = 7.2
2. 6.4x + 2.75 = -10.05
3. 7 = 14.5 - 2x
4. 25 - 10x = 45
5. -x + 15 = 9
6. 3.5 = 4x - 10.75
7. -16 = 2.85 - 1.25x
8. -24x - 36 = -72
9. -2.6x + 6.5 = 0
10. (1/2)x - (2/5) = -3/10
11. 2 1/8 + 6 1/4 x = -3 1/2

Explanation:

Step1: Solve equation 5: \(-3x + 5.4 = 7.2\)

Subtract \(5.4\) from both sides: \(-3x = 7.2 - 5.4 = 1.8\)
Divide by \(-3\): \(x = \frac{1.8}{-3} = -0.6\)

Step2: Solve equation 6: \(6.4x + 2.75 = -10.05\)

Subtract \(2.75\): \(6.4x = -10.05 - 2.75 = -12.8\)
Divide by \(6.4\): \(x = \frac{-12.8}{6.4} = -2\)

Step3: Solve equation 7: \(7 = 14.5 - 2x\)

Subtract \(14.5\): \(-7.5 = -2x\)
Divide by \(-2\): \(x = \frac{7.5}{2} = 3.75\)

Step4: Solve equation 8: \(25 - 10x = 45\)

Subtract \(25\): \(-10x = 20\)
Divide by \(-10\): \(x = -2\)

Step5: Solve equation 9: \(-x + 15 = 9\)

Subtract \(15\): \(-x = -6\)
Multiply by \(-1\): \(x = 6\)

Step6: Solve equation 10: \(3.5 = 4x - 10.75\)

Add \(10.75\): \(14.25 = 4x\)
Divide by \(4\): \(x = \frac{14.25}{4} = 3.5625\)

Step7: Solve equation 11: \(-16 = 2.85 - 1.25x\)

Subtract \(2.85\): \(-18.85 = -1.25x\)
Divide by \(-1.25\): \(x = \frac{18.85}{1.25} = 15.08\)

Step8: Solve equation 12: \(-24x - 36 = -72\)

Add \(36\): \(-24x = -36\)
Divide by \(-24\): \(x = \frac{36}{24} = 1.5\)

Step9: Solve equation 13: \(-2.6x + 6.5 = 0\)

Subtract \(6.5\): \(-2.6x = -6.5\)
Divide by \(-2.6\): \(x = \frac{6.5}{2.6} = 2.5\)

Step10: Solve equation 14: \(\frac{1}{2}x - \frac{2}{5} = -\frac{3}{10}\)

Add \(\frac{2}{5}\) (which is \(\frac{4}{10}\)): \(\frac{1}{2}x = -\frac{3}{10} + \frac{4}{10} = \frac{1}{10}\)
Multiply by \(2\): \(x = \frac{2}{10} = \frac{1}{5} = 0.2\)

Step11: Solve equation 15: \(2\frac{1}{8} + 6\frac{1}{4}x = -3\frac{1}{2}\)

Convert to improper fractions: \(\frac{17}{8} + \frac{25}{4}x = -\frac{7}{2}\)
Subtract \(\frac{17}{8}\): \(\frac{25}{4}x = -\frac{7}{2} - \frac{17}{8} = -\frac{28}{8} - \frac{17}{8} = -\frac{45}{8}\)
Multiply by \(\frac{4}{25}\): \(x = -\frac{45}{8} \times \frac{4}{25} = -\frac{9}{10} = -0.9\)

Answer:

1. \(x = -0.6\)
2. \(x = -2\)
3. \(x = 3.75\)
4. \(x = -2\)
5. \(x = 6\)
6. \(x = 3.5625\)
7. \(x = 15.08\)
8. \(x = 1.5\)
9. \(x = 2.5\)
10. \(x = 0.2\) (or \(\frac{1}{5}\))
11. \(x = -0.9\) (or \(-\frac{9}{10}\))