Let's solve each of the given linear equations step-by-step:

a. $9 - 6x = -1$

1. Subtract 9 from both sides: $9 - 6x - 9 = -1 - 9$ $-6x = -10$
2. Divide both sides by -6: $x = \frac{-10}{-6} = \frac{10}{6} = \frac{5}{3}$ So, $x = \frac{5}{3}$.

b. $-5x - 4.2 = 7.4$

1. Add 4.2 to both sides: $-5x - 4.2 + 4.2 = 7.4 + 4.2$ $-5x = 11.6$
2. Divide both sides by -5: $x = \frac{11.6}{-5} = -2.32$ So, $x = -2.32$.

c. $2 = 11 - 3x$

1. Subtract 11 from both sides: $2 - 11 = 11 - 11 - 3x$ $-9 = -3x$
2. Divide both sides by -3: $x = \frac{-9}{-3} = 3$ So, $x = 3$.

d. $-3 = -6x - 8$

1. Add 8 to both sides: $-3 + 8 = -6x - 8 + 8$ $5 = -6x$
2. Divide both sides by -6: $x = \frac{5}{-6} = -\frac{5}{6}$ So, $x = -\frac{5}{6}$.

e. $-1 = 4 - 4x$

1. Subtract 4 from both sides: $-1 - 4 = 4 - 4 - 4x$ $-5 = -4x$
2. Divide both sides by -4: $x = \frac{-5}{-4} = \frac{5}{4}$ So, $x = \frac{5}{4}$.

f. $35 - 13x = -5$

1. Subtract 35 from both sides: $35 - 35 - 13x = -5 - 35$ $-13x = -40$
2. Divide both sides by -13: $x = \frac{-40}{-13} = \frac{40}{13}$ So, $x = \frac{40}{13}$.

Summary

• $a. x = \frac{5}{3}$
• $b. x = -2.32$
• $c. x = 3$
• $d. x = -\frac{5}{6}$
• $e. x = \frac{5}{4}$
• $f. x = \frac{40}{13}$

Would you like more details on any specific solution or have any questions? Here are some related questions you might ask:

1. How do you solve systems of linear equations?
2. Can you explain the steps for solving quadratic equations?
3. What is the method to solve equations involving fractions?
4. How do you solve linear inequalities?
5. Can you show examples of word problems involving linear equations?

Tip

When solving linear equations, always isolate the variable on one side of the equation by performing inverse operations step-by-step.