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Task 10: Simplify and solve the equations

a) $5x - 4 + 3x = 16 + 2x + 40$
Simplify both sides: $8x - 4 = 58 + 2x$ Bring like terms together: $8x - 2x = 58 + 4$ $6x = 62 \quad \Rightarrow \quad x = \frac{62}{6} = \frac{31}{3}$

b) $x + 3 + 2x + 7 = 3 + 4x - 10$
Simplify both sides: $3x + 10 = -7 + 4x$ Bring like terms together: $3x - 4x = -7 - 10$ $-x = -17 \quad \Rightarrow \quad x = 17$

c) $3x + 4 - 5x = -12 + 3x - 19$
Simplify both sides: $-2x + 4 = -31 + 3x$ Bring like terms together: $-2x - 3x = -31 - 4$ $-5x = -35 \quad \Rightarrow \quad x = 7$

d) $9x - 4 - x = 2x - 10 + 4x - x + 3$
Simplify both sides: $8x - 4 = 5x - 7$ Bring like terms together: $8x - 5x = -7 + 4$ $3x = -3 \quad \Rightarrow \quad x = -1$

Task 11: Expand the parentheses and solve the equations

a) $3(x + 2) = 5x$
Expand: $3x + 6 = 5x$ Bring like terms together: $6 = 5x - 3x$ $6 = 2x \quad \Rightarrow \quad x = 3$

b) $4(x - 1) = 2(x - 3)$
Expand: $4x - 4 = 2x - 6$ Bring like terms together: $4x - 2x = -6 + 4$ $2x = -2 \quad \Rightarrow \quad x = -1$

c) $3(3 + 4x) = 5(2x + 3)$
Expand: $9 + 12x = 10x + 15$ Bring like terms together: $12x - 10x = 15 - 9$ $2x = 6 \quad \Rightarrow \quad x = 3$

d) $2x - (x - 3) = 3x - (17 - 2x)$
Expand: $2x - x + 3 = 3x - 17 + 2x$ Simplify: $x + 3 = 5x - 17$ Bring like terms together: $x - 5x = -17 - 3$ $-4x = -20 \quad \Rightarrow \quad x = 5$

e) $2(5x + 2) = 9x - (x - 9)$
Expand: $10x + 4 = 9x - x + 9$ Simplify: $10x + 4 = 8x + 9$ Bring like terms together: $10x - 8x = 9 - 4$ $2x = 5 \quad \Rightarrow \quad x = \frac{5}{2}$

Task 12: Solve the equations

a) $0.5x = 3$
$x = \frac{3}{0.5} = 6$

b) $0.3x = 1.2$
$x = \frac{1.2}{0.3} = 4$

c) $x - 2.8 = 0.7$
$x = 0.7 + 2.8 = 3.5$

d) $1.3 - 2x = 5.9$
$-2x = 5.9 - 1.3$ $-2x = 4.6 \quad \Rightarrow \quad x = \frac{-4.6}{2} = -2.3$

e) $1.8x - 0.9 = 0.6x + 1.5$
Bring like terms together: $1.8x - 0.6x = 1.5 + 0.9$ $1.2x = 2.4 \quad \Rightarrow \quad x = \frac{2.4}{1.2} = 2$

If you need further clarification or detailed explanations for any of these, let me know!

Here are 5 related questions:

1. How can I verify the solutions for equations with variables on both sides?
2. What are the steps to solve equations with decimals or fractions?
3. How can I simplify expressions before solving equations?
4. What is the importance of checking solutions in the original equation?
5. How do parentheses affect solving equations?

Tip: Always simplify both sides of an equation as much as possible before isolating the variable!